The irregularity of graphs under graph operations

Abdo, Hosam; Dimitrov, Darko

doi:10.7151/dmgt.1733

Cited by 39 publications

(22 citation statements)

References 12 publications

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“…The results presented in this paper complement the results from [3]. Here we consider the total irregularity of simple undirected graphs under several graph operations.…”

Section: Resultssupporting

confidence: 73%

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The Total Irregularity of Some Composite Graphs

Abdo¹,

Dimitrov²

2015

IJCA

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The total irregularity of a simple undirected graphis the degree of the vertex u. In this paper we investigate the change of the total irregularity of graphs under various subdivision operations. Also, we present exact expressions and upper bounds on the total irregularity of different composite graphs such as the double graph, the extended double cover of a graph, the generalized thorn graph, several variants of subdivision corona graphs, and the hierarchical product graphs.

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“…The results presented in this paper complement the results from [3]. Here we consider the total irregularity of simple undirected graphs under several graph operations.…”

Section: Resultssupporting

confidence: 73%

“…Moreover, if G is a tree, then it was shown that irr t (G) ≤ (n − 2) irr(G). A lot of researches on irregularity of graphs have been carried out recently [2,3,7]. In this work we investigate the change of the total irregularity under different graph operations.…”

Section: Introductionmentioning

confidence: 99%

The Total Irregularity of Some Composite Graphs

Abdo¹,

Dimitrov²

2015

IJCA

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“…Recently, Abdo et al introduced the new term "total irregularity measure of a graph G", which is defined as IRR t (G) � 1/2 UV∈E |d u − d v | [34][35][36]. Recently, Gutman introduced the IRF(G) irregularity index of the graph G, which is described as IRF(G) � UV∈E (d u − d v ) 2 in [37].…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Molecular Irregularity Indices of Nanostar, Fullerene, and Polymer Dendrimers

Quan

Wang

Munir

et al. 2020

Journal of Chemistry

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Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. Some properties like toxicity, entropy, and heats of vaporization of these dendrimers can be forecasted using topological indices. e present article is devoted to study of irregularity indices of three well-known classes of dendrimers, namely, nanostar dendrimer D [p], fullerene dendrimer NS 4 [p], and polymer dendrimerNS 5 [p], where p is the step size. We also see the relation of irregularity of these dendrimers on the step size graphically.

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“…Let V = V (P n ) = V (C ′ n ) and let B be an adjacency basis of P n . Since for two different vertices x, y ∈ V , d C ′ n ,2 (x, y) = d Pn,2 (x, y) if and only if x, y ∈ {v 1…”

Section: Lemma 12mentioning

confidence: 99%

Simultaneous Resolvability in Families of Corona Product Graphs

Ramírez-Cruz¹,

Estrada‐Moreno²,

Rodríguez-Velázquez³

2016

Bull. Malays. Math. Sci. Soc.

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Let G be a graph family defined on a common vertex set V and let d be a distance defined on every graph G ∈ G. A set S ⊂ V is said to be a simultaneous metric generator for G if for every G ∈ G and every pair of different vertices u, v ∈ V there exists s ∈ S such that d(s, u) = d(s, v). The simultaneous metric dimension of G is the smallest integer k such that there is a simultaneous metric generator for G of cardinality k. We study the simultaneous metric dimension of families composed by corona product graphs. Specifically, we focus on the case of two particular distances defined on every G ∈ G, namely, the geodesic distance d G and the distance d G,2 : V × V → N ∪ {0} defined as d G,2 (x, y) = min{d G (x, y), 2}.

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The irregularity of graphs under graph operations

Cited by 39 publications

References 12 publications

The Total Irregularity of Some Composite Graphs

The Total Irregularity of Some Composite Graphs

Molecular Irregularity Indices of Nanostar, Fullerene, and Polymer Dendrimers

Simultaneous Resolvability in Families of Corona Product Graphs

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