1–20 of
129 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...

Diamantis Koreas
V.G. Vizing showed that any graph belongs to one of two classes: Class 1 if χʹ(G) = Δ(G) or in class 2 if χʹ(G) = Δ(G) + 1, where χʹ(G) and Δ(G) denote the edge chromatic index of G and the maximum de...

S. Susilawati
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Edy Tri Baskoro
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Rinovia Simanjuntak
In 2010, Nurdin, Baskoro, Salman and Gaos conjectured that the total vertex irregularity strength of any tree T is determined only by the number of vertices of degrees 1, 2 and 3 in T. This paper will...

Hafizh M. Radiapradana
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Suhadi Wido Saputro
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Erma Suwastika
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Oki Neswan
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Andrea SemanicovaFenovcıkova
For integer k ≥ 2, let X = {0, 1, 2, …, k}. In this paper, we determine the order of a star graph K1, n of n + 1 vertices, such that K1, n admits a topological integer additive setlabeling (TIASL) wi...

Chithra Mr
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Manju K. Menon
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A. Vijayakumar
Many graphs such as hypercubes, star graphs, pancake graphs, grid, torus etc are known to be good interconnection network topologies. In any network topology, the vertices represent the processors and...

Leomarich F. Casinillo
Let G = (V(G), E(G)) be a path of order n ≥ 1. Let fm(G) be a path with m ≥ 0 independent dominating vertices which follows a Fibonacci string of binary numbers where 1 is the dominating vertex. A set...