Extremal Values of Randić Index among Some Classes of Graphs

Extremal Values of Randić Index among Some Classes of Graphs

Suppose G is a simple graph with edge set EG. The Randić index RG is defined as RG=∑uv∈EG1/degGudegGv, where degGu and degGv denote the vertex degrees of u and v in G, respectively. In this paper, the first and second maximum of Randić index among all n−vertex c−cyclic graphs was computed. As a cons...

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Main Authors: Ali Ghalavand, Ali Reza Ashrafi, Marzieh Pourbabaee
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2021/7758172
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spelling doaj-ceb98eefe99a473d99f9664a01e492d12021-06-28T01:50:56ZengHindawi LimitedMathematical Problems in Engineering1563-51472021-01-01202110.1155/2021/7758172Extremal Values of Randić Index among Some Classes of GraphsAli Ghalavand0Ali Reza Ashrafi1Marzieh Pourbabaee2Department of Pure MathematicsDepartment of Pure MathematicsDepartment of Applied MathematicsSuppose G is a simple graph with edge set EG. The Randić index RG is defined as RG=∑uv∈EG1/degGudegGv, where degGu and degGv denote the vertex degrees of u and v in G, respectively. In this paper, the first and second maximum of Randić index among all n−vertex c−cyclic graphs was computed. As a consequence, it is proved that the Randić index attains its maximum and second maximum on two classes of chemical graphs. Finally, we will present new lower and upper bounds for the Randić index of connected chemical graphs.http://dx.doi.org/10.1155/2021/7758172
collection DOAJ
language English
format Article
sources DOAJ
author Ali Ghalavand
Ali Reza Ashrafi
Marzieh Pourbabaee
spellingShingle Ali Ghalavand
Ali Reza Ashrafi
Marzieh Pourbabaee
Extremal Values of Randić Index among Some Classes of Graphs
Mathematical Problems in Engineering
author_facet Ali Ghalavand
Ali Reza Ashrafi
Marzieh Pourbabaee
author_sort Ali Ghalavand
title Extremal Values of Randić Index among Some Classes of Graphs
title_short Extremal Values of Randić Index among Some Classes of Graphs
title_full Extremal Values of Randić Index among Some Classes of Graphs
title_fullStr Extremal Values of Randić Index among Some Classes of Graphs
title_full_unstemmed Extremal Values of Randić Index among Some Classes of Graphs
title_sort extremal values of randić index among some classes of graphs
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1563-5147
publishDate 2021-01-01
description Suppose G is a simple graph with edge set EG. The Randić index RG is defined as RG=∑uv∈EG1/degGudegGv, where degGu and degGv denote the vertex degrees of u and v in G, respectively. In this paper, the first and second maximum of Randić index among all n−vertex c−cyclic graphs was computed. As a consequence, it is proved that the Randić index attains its maximum and second maximum on two classes of chemical graphs. Finally, we will present new lower and upper bounds for the Randić index of connected chemical graphs.
url http://dx.doi.org/10.1155/2021/7758172
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AT alirezaashrafi extremalvaluesofrandicindexamongsomeclassesofgraphs
AT marziehpourbabaee extremalvaluesofrandicindexamongsomeclassesofgraphs
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