1–20 of
114 results.

Suresh Elumalai
•
Toufik Mansour
•
Mohammad Ali Rostami
Journal article
• 2018
English
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
Journal article
• 2018
English
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
•
Italo J. Dejter
•
Carlos A. Araujo
Journal article
• 2018
English
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
Journal article
• 2018
English
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
•
Saeid Alikhani
Journal article
• 2018
English
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
•
Julian A. Allagan
Journal article
• 2018
English
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
•
Hamid Reza Ellahi
•
Gholam Hossein FathTabar
•
Ahmad Gholami
Journal article
• 2018
English
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
•
Suma A. S.
Journal article
• 2018
English
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
•
Howard Skogman
Journal article
• 2018
English
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
•
Ashok Gupta
•
Rinovia Simanjuntak
Journal article
• 2018
English
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
•
Alfi Y. Zakiyyah
Journal article
• 2018
English
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
•
Nima Ghanbari
•
Saeid Alikhani
Journal article
• 2018
English
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
•
Andrea SemanicovaFenovcikova
•
S. Slamin
•
Kiki A. Sugeng
Journal article
• 2018
English
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
•
Mattias Eriksson
Journal article
• 2018
English
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
•
Shariefuddin Pirzada
Journal article
• 2018
English
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...

Driscoll, Keith
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Krop, Elliot
•
Nguyen, Michelle
Journal article
• 2017
English
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 ...

Lusiani, Anie
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Baskoro, Edy Tri
•
Saputro, Suhadi Wido
Journal article
• 2017
English
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...

Valette, Alain
Journal article
• 2017
English
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...

P, Padmapriya
•
Mathad, Veena
Journal article
• 2017
English
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...

Pravas, K
•
Vijayakumar, A
Journal article
• 2017
English
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...