1–100 of
114 results.

Suresh Elumalai
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Toufik Mansour
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Mohammad Ali Rostami
The hyperZagreb index of a simple connected graph G is defined by ${\chi ^2}(G) = \sum_{uv \in E(G)} {{{\left( {d(u) + d(v)} \right)}^2}}$. In this paper, we establish, analyze and compare some new u...

Vladimir Dimitrov Samodivkin
The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number. We obtain sufficient conditions for the validity of the ineq...

Luis R. Fuentes
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Italo J. Dejter
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Carlos A. Araujo
Let $0<n\in\mathbb{Z}$. In the unit distance graph of $\mathbb{Z}^n\subset\mathbb{R}^n$, a perfect dominating set is understood as having induced components not necessarily trivial. A modification ...

Sudip Bera
Given a group G, the intersection power graph of G, denoted by $\mathcal{G}_I(G)$, is the graph with vertex set G and two distinct vertices x and y are adjacent in $\mathcal{G}_I(G)$ if there exists ...

Somayeh Jahari
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Saeid Alikhani
Let G be a simple graph of order n. The domination polynomial of G is the polynomial $D(G, x)=\sum_{i=\gamma(G)}^{n} d(G,i) x^{i}$, where d(G,i) is the number of dominating sets of G of size i and $\g...

Eunice MphakoBanda
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Julian A. Allagan
We give some reduction formulas for computing the Tutte polynomial of any graph with parallel classes. Several examples are given to illustrate our results.

Ramin Nasiri
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Hamid Reza Ellahi
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Gholam Hossein FathTabar
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Ahmad Gholami
The signless Laplacian Estrada index of a graph $G$ is defined as $SLEE(G)=\sum^{n}_{i=1}e^{q_i}$ where $q_1, q_2, \ldots, q_n$ are the eigenvalues of the signless Laplacian matrix of G. Following th...

B. Sooryanarayana
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Suma A. S.
Let G=(V,E) be a simple connected graph. A subset S of V is called a neighbourhood set of G if $G=\bigcup_{s\in S}<N[s]>$, where N[v] denotes the closed neighbourhood of the vertex v in G. Furth...

Marvin Minei
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Howard Skogman
We give a new construction of Ramanujan graphs using a generalized type of covering graph called a weighted covering graph. For a given prime p the basic construction produces bipartite Ramanujan grap...

Ali Ahmad
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Ashok Gupta
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Rinovia Simanjuntak
In computer science, graphs are used in variety of applications directly or indirectly. Especially quantitative labeled graphs have played a vital role in computational linguistics, decision making so...

Nobuaki Obata
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Alfi Y. Zakiyyah
A connected graph is said to be of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a g...

Ali Sadeghieh
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Nima Ghanbari
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Saeid Alikhani
Let G be a finite connected graph of order n. The Gutman index Gut(G) of G is defined as $\sum_{\{x,y\}\subseteq V(G)}deg(x)deg(y)d(x, y)$, where deg(x) is the degree of vertex x in G and d(x, y) is t...

Martin Baca
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Andrea SemanicovaFenovcikova
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S. Slamin
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Kiki A. Sugeng
For a simple graph G, a vertex labeling f:V(G)\to {1, 2, ..., k} is called a klabeling. The weight of a vertex v, denoted by $wt_f(v)$ is the sum of all vertex labels of vertices in the closed neigh...

Håkan Lennerstad
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Mattias Eriksson
In this paper we consider node labelings c of an undirected connected graph G=(V,E) with labels {1,2,... ,V}, which induce a list distance c(u,v)=c(v)c(u) besides the usual graph distance d(u,v)....

Uma Tul Samee
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Shariefuddin Pirzada
A $k$partite $r$digraph(multipartite multidigraph) (or briefly MMD)($k\geq 3$, $r\geq 1$) is the result of assigning a direction to each edge of a $k$partite multigraph that is without loops and co...

Thodoris Karatasos
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Evi Papaioannou
In this work, we present an innovative image recognition technique which is based on the exploitation of transitdata in images or simple photographs of sites of interest. Our objective is to automati...

I. Nengah Suparta
A Gray code of length n is a list of all binary words of length n such that each two successive codewords differ in only one bit position. If the first and the last codewords also share this property,...

V. Yegnanarayanan
Let $p \ge 3$ be a positive integer and let $k \in {1, 2, ..., p1} \ \lfloor p/2 \rfloor$. The generalized Petersen graph GP(p,k) has its vertex and edge set as $V(GP(p, k)) = \{u_i : i \in Zp\} \cup...

Kijung Kim
In 2010, Kim, Park and Sano studied the competition numbers of Johnson graphs. They gave the competition numbers of J(n,2) and J(n,3).In this note, we consider the competition number of J(n,4).

Faraha Ashraf
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Martin Baca
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Andrea SemanicovaFenovcikova
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Ayesha Shabbir
A simple graph G=(V(G),E(G)) admits an Hcovering if every edge in E(G) belongs at least to one subgraph of G isomorphic to a given graph H. Then the graph G admitting Hcovering admits an Hirregular...

Suk J. Seo
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Peter J. Slater
A distinguishing set for a graph G = (V, E) is a dominating set D, each vertex $v \in D$ being the location of some form of a locating device, from which one can detect and precisely identify any give...

Steven Schluchter
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J. Z. Schroeder
A proper embedding of a graph G in a pseudosurface P is an embedding in which the regions of the complement of G in P are homeomorphic to discs and a vertex of G appears at each pinchpoint in P; we s...

Mustapha Aouchiche
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Pierre Hansen
The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007) 6067] that $\eta \le n  D$, where $...

Mehdi Alaeiyan
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Ayoob Mehrabani
Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect mcoloring of a graph G with m colors is a partition of the vertex set of G into m parts A_...

Radosław Cymer
In decomposition theory, extreme sets have been studied extensively due to its connection to perfect matchings in a graph. In this paper, we first define extreme sets with respect to degreematchings ...

Amrita Acharyya
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Jon M. Corson
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Bikash Das
We generalize the idea of cofinite groups, due to B. Hartley, [2]. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions.The ...

Hamed Ghasemian Zoeram
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Daniel Yaqubi
A vertex of degree one is called an endvertex and the set of endvertices of G is denoted by End(G). For a positive integer k, a tree T be called kended tree if $End(T) \leq k$. In this paper, we ...

Kamal Lochan Patra
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Binod Kumar Sahoo
This paper is a survey on the upper and lower bounds for the largest eigenvalue of the Laplacian matrix, known as the Laplacian spectral radius, of a graph. The bounds are given as functions of graph ...

PhanThuan Do
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NgocKhang Le
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VanThieu Vu
Trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. Many NPhard problems can be solved in polynomial time if they are restricted on trapezoid graphs. A matching in a ...

Keith Driscoll
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Elliot Krop
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Michelle Nguyen
For any integer $k>0$, a tree $T$ is $k$cordial if there exists a labeling of the vertices of $T$ by $\mathbb{Z}_k$, inducing edgeweights as the sum modulo $k$ of the labels on incident vertices ...

Debdas Mishra
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Sushant Kumar Rout
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Puma Chandra Nayak
Here we denote a {\it diameter six tree} by $(c; a_{1}, a_{2}, \ldots, a_{m}; b_{1}, b_{2}, \ldots, b_{n}; c_{1}, c_{2}, \ldots, c_{r})$, where $c$ is the center of the tree; $a_{i}, i = 1, 2, \ldo...

S. M. Hosseini Moghaddam
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D. A. Mojdeh
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Babak Samadi
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Lutz Volkmann
In this paper, we study the signed 2independence number in graphs and give new sharp upper and lower bounds on the signed 2independence number of a graph by a simple uniform approach. In this way, w...

Seyed Morteza Mirafzal
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Ali Zafari
Let $\Gamma=Cay(\mathbb{Z}_n, S_k)$ be the Cayley graph on the cyclic additive group $\mathbb{Z}_n$ $(n\geq 4),$ where $S_1=\{1, n1\}$, \dots , $S_k=S_ {k1}\cup\{k, nk\}$ are the inverseclosed s...

Vladimir R. Rosenfeld
A {\em retractingfree bidirectional circuit} in a graph $G$ is a closed walk which traverses every edge exactly once in each direction and such that no edge is succeeded by the same edge in the oppos...

Alain Valette
For a finite connected graph $X$, we consider the graph $RX$ obtained from $X$ by associating a new vertex to every edge of $X$ and joining by edges the extremities of each edge of $X$ to the correspo...

Omid Khormali
For any $k \in \mathbb{N}$, the $k$distance graph $D^{k}G$ has the same vertex set of $G$, and two vertices of $D^{k}G$ are adjacent if they are exactly distance $k$ apart in the original graph $G$. ...

Denny Riama Silaban
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Edy Tri Baskoro
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Saladin Uttunggadewa
Let $G$ and $H$ be simple graphs. The Ramsey number for a pair of graph $G$ and $H$ is the smallest number $r$ such that any redblue coloring of edges of $K_r$ contains a red subgraph $G$ or a blue s...

Nader Jafari Rad
A subset $X$ of edges of a graph $G$ is called an \textit{edgedominating set} of $G$ if every edge not in $X$ is adjacent tosome edge in $X$. The edge domination number $\gamma'(G)$ of $G$ is the mini...

Ali Reza Ashrafi
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Ahmad Gholami
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Zeinab Mehranian
The power graph $\mathcal{P}(G)$ of a group $G$ is the graphwith group elements as vertex set and two elements areadjacent if one is a power of the other. The aim of this paper is to compute the autom...

Monther Rashed Alfuraidan
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Yusuf F. Zakariya
Let $(\Gamma,*)$ be a finite group and $S$ a possibly empty subset of $\Gamma$ containing its nonselfinvertible elements. In this paper, we introduce the inverse graph associated with $\Gamma$ whose...

Anie Lusiani
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Edy Tri Baskoro
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Suhadi Wido Saputro
Let $K_{l\times t}$ be a complete, balanced, multipartite graph consisting of $l$ partite sets and $t$ vertices in each partite set. For given two graphs $G_1$ and $G_2$, and integer $j\geq 2$, the si...

Padmapriya P.
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Veena Mathad
Let $G = (V,E)$ be a simple connected graph. Theeccentricdistance sum of $G$ is defined as$\xi^{ds}(G) =\ds\sum_{\{u,v\}\subseteq V(G)} [e(u)+e(v)] d(u,v)$, where $e(u)$ %\dsis the eccentricity of th...

K. Pravas
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A. Vijayakumar
The Gallai and the antiGallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes...

Anak Agung Gede Ngurah
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Rinovia Simanjuntak
A graph G of order p and size q is called super edgemagic if there exists a bijective function f from V(G) U E(G) to {1, 2, 3, ..., p+q} such that f(x) + f(xy) + f(y) is a constant for every edge $xy...

Bryan Freyberg
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Melissa Keranen
The following generalization of distance magic graphs was introduced in [2]. A directed Z_ndistance magic labeling of an oriented graph $\overrightarrow{G}=(V,A)$ of order n is a bijection $\overrigh...

Richard M. Low
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W. H. Chan
The combinatorial game of Nim can be played on graphs. Over the years, various Nimlike games on graphs have been proposed and studied by N.J. Calkin et al., L.A. Erickson and M. Fukuyama. In this pap...

R. Rajarajachozhan
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R. Sampathkumar
A twin edge $k\!$coloring of a graph $G$ is a proper edge $k$coloring of $G$ with the elements of $\mathbb{Z}_k$ so that the induced vertex $k$coloring, in which the color of a vertex $v$ in $G$ is...

Ebrahim Vatandoost
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Fatemeh Ramezani
Let $R$ be a commutative ring (with 1) and let $Z(R)$ be its set of zerodivisors. The zerodivisor graph $\Gamma(R)$ has vertex set $Z^*(R)=Z(R) \setminus \lbrace0 \rbrace$ and for distinct $x,y \in ...

Bart Demoen
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PhuongLan Nguyen
A graph edge is $d$coloring redundant if the removal of the edge doesnot change the set of $d$colorings of the graph. Graphs that are toosparse or too dense do not have coloring redundant edges. Tig...

Linda Eroh
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Henry Escuadro
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Ralucca Gera
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Samuel Prahlow
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Karl Schmitt
Due to the increasing discovery and implementation of networks within all disciplines of life, the study of subgraph connectivity has become increasingly important. Motivated by the idea of community ...

M. H. Akhbari
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Nader Jafari Rad
A set $D$ of vertices in a graph $G=(V,E)$ is a total dominatingset if every vertex of $G$ is adjacent to some vertex in $D$. Atotal dominating set $D$ of $G$ is said to be weak if everyvertex $v\in V...

Shariefuddin Pirzada
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Hilal A. Ganie
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Merajuddin Siddique
For a graph $G$ with vertex set $V(G)=\{v_1, v_2, \dots, v_n\}$, let $S$ be the covering set of $G$ having the maximum degree over all the minimum covering sets of $G$. Let $N_S[v]=\{u\in S : uv \in E...

J. Vernold Vivin
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K. Kaliraj
The notion of equitable colorability was introduced by Meyer in $1973$ \cite{meyer}. In this paper we obtain interesting results regarding the equitable chromatic number $\chi_{=}$ for the corona grap...

Charles Delorme
We revisit Hoffman relation involving chromatic number $\chi$ and eigenvalues. We construct some graphs and weighted graphs such that the largest and smallest eigenvalues $\lambda$ dan $\mu$ satisfy $...

N. S. A. Karim
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Roslan Hasni
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GeeChoon Lau
For a graph $G$, let $P(G,\lambda)$ denote the chromatic polynomial of $G$. Two graphs $G$ and $H$ are chromatically equivalent if they share the same chromatic polynomial. A graph $G$ is chromaticall...

Salman Fawzi Ghazal
Let $D$ be a digraph without digons. Seymour's second neighborhood conjecture states that $D$ has a vertex $v$ such that $d^+(v) \leq d^{++}(v)$. Under some conditions, we prove this conjecture for di...

David J. Aldous
Modeling a road network as a planar graph seems very natural. However, in studying continuum limits of such networks it is useful to take {\em routes} rather than {\em edges} as primitives. This artic...

Christian Barrientos
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Sarah M. Minion
In this paper we study a technique to transform $\alpha $labeled trees into $\rho $labeled forests. We use this result to prove that the complete graph $K_{2n+1}$ can be decomposed into these types...

Ismail Sahul Hamid
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S. Balamurugan
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A. Navaneethakrishnan
A set $S$ of vertices of a graph $G$ such that $\left\langle S\right\rangle$ has an isolated vertex is called an \emph{isolate set} of $G$. The minimum and maximum cardinality of a maximal isolate set...

Chula Janak Jayawardene
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Edy Tri Baskoro
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Lilanthi Samarasekara
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Syafrizal Sy
For simple graphs $G_1$ and $G_2$, the size Ramsey multipartite number $m_j(G_1, G_2)$ is defined as the smallest natural number $s$ such that any arbitrary two coloring of the graph $K_{j \times s}$ ...

Maryam Atapour
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Seyyed Mahmoud Sheikholeslami
A nonnegative signed dominating function (NNSDF) of a graph $G$is a function $f$ from the vertex set $V(G)$ to the set $\{1,1\}$such that $\sum_{u\in N[v]}f(u)\ge 0$ for every vertex $v\inV(G)$. The ...

Ioan Tomescu
In this paper, we show that in the classof connected graphs $G$ of order $n\geq 3$ having girth at least equal to $k$, $3\leq k\leq n$, the unique graph $G$ having minimum general sumconnectivity ind...

Chandrashekar Adiga
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Rakshith B. R.
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K.N., Subba Krishna
In this paper we define extended corona and extended neighborhoodcorona of two graphs $G_{1}$ and $G_{2}$, which are denoted by$G_{1}\bullet G_{2}$ and $G_{1}\ast G_{2}$ respectively. Wecompute their ...

Sung Sik U.
This paper discusses the enumeration for rooted spanning trees and forests of the labelled join graphs $K_m+H_n$ and $K_m+K_{n,p}$, where $H_n$ is a graph with $n$ isolated vertices.

Michael Haythorpe
A constructive method is provided that outputs a directed graph which is named a broken crown graph, containing $5n9$ vertices and $k$ Hamiltonian cycles for any choice of integers $n \geq k \geq 4$....

Jeremy Moody
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P. K. Aravind
This paper shows how a method developed by Van Steenwijk can be generalized to calculate the resistance between any two vertices of a symmetrical polytope all of whose edges are identical resistors. T...

Christian Rubio Montiel
A graph $G$ is \emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number) $\alpha(G)$ equals the number of (maxim...

Seyed Mahmoud Sheikholeslami
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Lutz Volkmann
Let $D$ be a finite and simple digraph with vertex set $V(D)$.A {\em signed Roman dominating function} on the digraph $D$ isa function $f:V (D)\longrightarrow \{1, 1, 2\}$ such that$\sum_{u\in N^[v...

Rafael Del Valle Vega
The BrualdiShen Conjecture on Eulerian Bipartite Tournaments states that any such graph can be decomposed into oriented 4cycles. In this article we prove the balanced case of the mentioned conjectur...

Gholam Hassan Shirdel
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Nasrin Kahkeshani
The purpose of the independent set interdiction problem in the weighted graph $G$ is to determine a set of vertices $R^*$ such that the weight of the maximum independent set in $GR^*$ is minimized. W...

Harishchandra S. Ramane
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Ashwini S. Yalnaik
The reciprocal complementary distance (RCD) matrix of a graph $G$ is defined as $RCD(G) = [rc_{ij}]$ where $rc_{ij} = \frac{1}{1+Dd_{ij}}$ if $i \neq j$ and $rc_{ij} = 0$, otherwise, where $D$ is the...

Jemal Abawajy
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Andrei Kelarev
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Joe Ryan
The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. This notion is motivated by its applications for the design of classication syste...

P. Anusha Devi
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S. Monikandan
An ecard of a graph $G$ is a subgraph formed by deleting an edge. A daecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph ...

Antoon H. Boode
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Hajo Broersma
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Jan F. Broenink
In this paper we introduce and study a directed tree problem motivated by a new graph product that we have recently introduced and analysed in two conference contributions in the context of periodic r...

Shariefuddin Pirzada
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Muhammad Ali Khan
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Zhou Guofei
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Koko K. Kayibi
A $k$hypertournament is a complete $k$hypergraph with each $k$edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a $k$hypertournament, the sc...

Xueliang Li
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Yongtang Shi
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Martin Trinks
The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a gr...

Hilal A. Ganie
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Shariefuddin Pirzada
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Edy Tri Baskoro
For a graph $G$ having adjacency spectrum ($A$spectrum) $\lambda_n\leq\lambda_{n1}\leq\cdots\leq\lambda_1$ and Laplacian spectrum ($L$spectrum) $0=\mu_n\leq\mu_{n1}\leq\cdots\leq\mu_1$, the energy...

Salman Ghazal
Seymour's second neighborhood conjecture states that every simple digraph (without digons) has a vertex whose first outneighborhood is at most as large as its second outneighborhood. Such a vertex i...

Sudev Naduvath
A setlabeling of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(X)$, where $X$ is a finite set and a setindexer of $G$ is a setlabeling such that the induced function $f^{\oplus}:E(G)...

Jonathan L. Gross
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Toufik Mansour
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Thomas W. Tucker
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David G. L. Wang
A Ringel ladder can be formed by a selfbaramalgamation operation on a symmetric ladder, that is, by joining the root vertices on its endrungs. The present authors have previously derived criteria u...

Kristiana Wijaya
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Edy Tri Baskoro
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Hilda Assiyatun
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Djoko Suprijanto
Let $F, G,$ and $H$ be nonempty graphs. The notation $F \rightarrow (G,H)$ means that if all edges of $F$ are arbitrarily colored by red or blue, then either the subgraph of $F$ induced by all red ed...

Clive Elphick
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Pawel Wocjan
This paper gives an errata to the paper "New measure of graph irregularity", Electronic Journal of Graph Theory and Applications {\bf 2}(1) (2014), 5265.

C. Dalfo
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M. A. Fiol
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M. Mitjana
We study a family of graphs related to the $n$cube. The middle cube graph of parameter k is the subgraph of $Q_{2k1}$ induced by the set of vertices whose binary representation has either $k1$ or $...

Colton Magnant
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Pouria Salehi Nowbandegani
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Hua Wang
Given a collection of $d$dimensional rectangular solids called blocks, no two of which sharing interior points, construct a block graph by adding a vertex for each block and an edge if the faces of t...

Anita Abildgaard Sillasen
The degree/diameter problem for directed graphs is the problem of determining the largest possible order for a digraph with given maximum outdegree d and diameter k. An upper bound is given by the Mo...

S. Arockiaraj
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P. Mahalakshmi
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P. Namasivayam
An injective function $f:V(G)\rightarrow \{0,1,2,\dots,q\}$ is an odd sum labeling if the induced edge labeling $f^*$ defined by $f^*(uv)=f(u)+f(v),$ for all $uv\in E(G),$ is bijective and $f^*(E(G))=...

Peter Recht
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Stefan Stehling
This paper addresses upper and lower bounds for the cardinality of a maximum vertex/edgedisjoint cycle packing in a polyhedral graph G. Bounds on the cardinality of such packings are provided, that ...

Ayesha Shabbir
In this note, we consider triangular, square and hexagonal lattices on the flat Klein bottle, and find subgraphs with the property that for any $j$ vertices there exists a longest path (cycle) avoidin...

Ashish K. Upadhyay
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Dipendu Maity
We present a necessary and sufficient condition for existence of edgedisjoint contractible Hamiltonian Cycles in the edge graph of polyhedral maps.

Yanbo Zhang
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Yaojun Chen
For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest integer $N$ such that for any graph $G$ of order $N$, either $G$ contains $F$ or the complement of $G$ contains $H$. Let $F...

Joe Demaio
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John Jacobson
In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci...

Dominique Buset
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Mirka Miller
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Oudone Phanalasy
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Joe Ryan
An antimagic labeling of a graph $G=(V,E)$ is a bijection from the set of edges $E$ to the set of integers $\{1,2,\dots, E\}$ such that all vertex weights are pairwise distinct, where the weight of ...

S. P. Subbiah
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J. Pandimadevi
An Hmagic labeling in an Hdecomposable graph G is a bijection f:V(G) U E(G) > {1,2, … ,p+q} such that for every copy H in the decomposition, $\sum\limits_{v\in V(H)} f(v)+\sum\limits_{e\in E(H)...

Cristina Dalfo
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Miquel Àngel Fiol
We study the (Delta,D) and (Delta,N) problems for doublestep digraphs considering the unilateral distance, which is the minimum between the distance in the digraph and the distance in its converse di...

Mustapha Chellali
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Nader Jafari Rad
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Suk Jai Seo
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Peter James Slater
A set D of vertices in a graph G = (V (G), E(G)) is an open neighborhood locatingdominating set (OLDset) for G if for every two vertices u, v of V (G) the sets N(u) ∩ D and N(v) ∩ D are nonempty an...

Anita Abildgaard Sillasen
A kgeodetic digraph G is a digraph in which, for every pair of vertices u and v (not necessarily distinct), there is at most one walk of length at most k from u to v. If the diameter of G is k, we sa...

Deepa Sinha
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Ayushi Dhama
A signed graph (or, $sigraph$ in short) is a graph G in which each edge x carries a value $\sigma(x) \in \{, +\}$ called its sign. Given a sigraph S, the negation $\eta(S)$ of the sigraph S is a sigr...

Henning Fernau
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Juan A. RodriguezVelazquez
In this paper, we show that several graph parameters are known in different areas under completely different names.More specifically, our observations connect signed domination, monopolies, $\alpha$d...

N. Paramaguru
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R. Sampathkumar
For k≥2, a modular kcoloring of a graph G without isolated vertices is a coloring of the vertices of G with the elements in Zk having the property that for every two adjacent vertices of G, the sums ...

Hebert PerezRoses
This paper discusses the most popular algebraic techniques and computational methods that have been used to construct large graphs with given degree and diameter.