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...

Ebrahim Vatandoost
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Masoumeh Khalili
Let G be a nonabelian group. The noncommuting graph of group G, shown by ΓG, is a graph with the vertex set G \ Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are a...

Martin Baca
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Muhammad Irfan
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Aisha Javed
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Andrea SemanicovaFenovcikova
For a simple graph G = (V, E) this paper deals with the existence of an edge labeling φ : E(G) → {0, 1, …, k − 1}, 2 ≤ k ≤ ∣E(G)∣, which induces a vertex labeling φ * : V(G) → {0, 1, …, k − 1} in suc...

Ju Zhou
A graph G is perfect matching transitive, shortly PMtransitive, if for any two perfect matchings M and N of G, there is an automorphism f : V(G) ↦ V(G) such that fe(M) = N, where fe(uv) = f(u)f(v). I...

SarahMarie Belcastro
We correct a small error in a 1996 paper of Albertson and Haas, and extend their lower bound for the fraction of properly colorable edges of planar subcubic graphs that are simple, connected, bridgele...