1–50 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...

HÃ¥kan 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_...

RadosÅ‚aw 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 ...

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...

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 ...

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 $G$. ...

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...

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 ...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...