41–60 of
114 results.

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
•
Edy Tri Baskoro
•
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.
•
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
•
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
•
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
•
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
•
Roslan Hasni
•
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
•
Hilal A. Ganie
•
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
•
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...

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
•
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...

Richard M. Low
•
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...

Linda Eroh
•
Henry Escuadro
•
Ralucca Gera
•
Samuel Prahlow
•
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 ...

Ebrahim Vatandoost
•
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
•
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...

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 $...

Ismail Sahul Hamid
•
S. Balamurugan
•
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
•
Edy Tri Baskoro
•
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 $K_{j \times s}$ ...