51–100 of
114 results.

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
•
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
•
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
•
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
•
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
•
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
•
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
•
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
•
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
•
Hajo Broersma
•
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
•
Muhammad Ali Khan
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Zhou Guofei
•
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
•
Yongtang Shi
•
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
•
Shariefuddin Pirzada
•
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
•
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
•
Pouria Salehi Nowbandegani
•
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
•
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
•
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
•
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
•
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
•
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
•
Mirka Miller
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Oudone Phanalasy
•
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
•
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
•
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
•
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
•
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
•
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
•
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.