Graphs with Equal Irregularity Indices

Dimitrov, Darko

doi:10.12700/aph.25.04.2014.04.4

Cited by 8 publications

(4 citation statements)

References 16 publications

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“…We encourage the interested reader to study references [7][8][9][10][11][12][13][14][15][16] for more details on these irregularity measures. Although some graphs with equal irregularity indices are presented in [17], there are some comparisons between these parameters in [18], which may imply the unreliability of them. In [19], relation between the chromatic number and irregularity measures was investigated.…”

Section: Introductionmentioning

confidence: 99%

Irregularity Measure of Graphs

Ghalavand

Gutman

Tavakoli

2023

Journal of Mathematics

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A simple graph G is said to be regular if its vertices have the same number of neighbors. Otherwise, G is nonregular. So far, various formulas, such as the Albertson index, total Albertson index, and degree deviation, have been introduced to quantify the irregularity of a graph. In this paper, we present sharp lower bounds for these indices in terms of the order, size, maximum degree, minimum degree, and forgotten and Zagreb indices of the underlying graph. We also prove that if G has the minimum value of degree deviation, among all nonregular n , m -graphs, then Δ G − δ G = 1 .

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Section: Introductionmentioning

confidence: 99%

Irregularity Measure of Graphs

Ghalavand

Gutman

Tavakoli

2023

Journal of Mathematics

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“…Gutman studied the topological indices and irregularity measures [27]. Graphs with equal irregularity indices are well explained [28]. Irregularity indices based on Zagreb indices were studied [29].…”

Section: Introductionmentioning

confidence: 99%

A Perspective Approach to Study the Valency-Based Irregular Indices for Benzenoid Planar Octahedron Structures

Rosary¹,

Alsinai

Siddiqui

et al. 2023

Journal of Chemistry

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The molecular topology and the chemical structures which are not regular perform a dominant character in designing the compound in connection with their physical and chemical properties. The study of topological descriptors of molecular structures is widely used in the field of cheminformatics, information technology, biomedical science, and many more. Numerous topological indices have been evolved in the theory of chemistry. Graphs which are not regular can be specified using irregular measures. In this article, we find some irregularity indices, which are useful in Quantitative structure activity relationship for benzenoid structures. Based on the exact analytic expressions, the numerical and graphical comparison for benzenoid structures is also provided.

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“…Various irregularity indices for dendrimer structures were established in [18] and for Probabilistic Neural Networks are established in [19]. Abdo et al [20] presented the graphs with maximal irregularity and the graphs with equal irregularity indices are presented by Dimitrov and Réti [21]. Moreover, Gutman presented irregularity for the various molecular graphs in [22].…”

Section: Introductionmentioning

confidence: 99%

Study of Topological Behavior of Some Computer Related Graphs

Ren¹,

Ahmed²,

Li³

2023

J. Comb. Math. Comb. Comput.

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Network theory is the study of graphs such as representing equilibrium relationships or unequal relationships between different objects. A network can be defined as a graph where nodes and / or margins have attributes (e.g. words). Topological index of a graph is a number that helps to understand its topology and a topological index is known as irregularity index if it is greater than zero and topological index of graph is equal to zero if and only if graph is regular. The irregularity indices are used for computational analysis of nonregular graph topological composition. In this paper, we aim to compute topological invariants of some computer related graph networks. We computed various irregularities indices for the graphs of OTIS swapped network \(OP_a\) and Biswapped Networks \(Bsw(Pa).\)

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Graphs with Equal Irregularity Indices

Cited by 8 publications

References 16 publications

Irregularity Measure of Graphs

Irregularity Measure of Graphs

A Perspective Approach to Study the Valency-Based Irregular Indices for Benzenoid Planar Octahedron Structures

Study of Topological Behavior of Some Computer Related Graphs

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