On leap Zagreb indices of bridge and chain graphs

Natarajan Chidambaram; Swathi Mohandoss; Xinjie Yu; Xiujun Zhang; Natarajan Chidambaram; Swathi Mohandoss; Xinjie Yu; Xiujun Zhang

doi:10.3934/math.2020420

AIMS Mathematics

2020, Volume 5, Issue 6: 6521-6536. doi: 10.3934/math.2020420

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On leap Zagreb indices of bridge and chain graphs

1.
Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam-612 001, Tamil Nadu, India
2.
School of Computer Science, Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu University, Chengdu, China

Received: 26 June 2020 Accepted: 13 August 2020 Published: 20 August 2020
MSC : 05C07, 05C35, 05C40

The 2-degree of a vertex v in a (molecular) graph G is the number of vertices which are at distance two from v in G. The first leap Zagreb index of a graph G is the sum of squares of the 2-degree of all vertices in G and the third leap Zagreb index of G is the sum of product of the degree and 2-degree of every vertex v in G. In this paper, we compute the first and third leap Zagreb indices of bridge and chain graphs. Also we apply these results to determine the first and third leap Zagreb indices of some chemical structures such as polyphenyl chains and spiro chains.
- leap Zagreb indices,
- bridge graphs,
- chain graph
Citation: Natarajan Chidambaram, Swathi Mohandoss, Xinjie Yu, Xiujun Zhang. On leap Zagreb indices of bridge and chain graphs[J]. AIMS Mathematics, 2020, 5(6): 6521-6536. doi: 10.3934/math.2020420

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Abstract

The 2-degree of a vertex v in a (molecular) graph G is the number of vertices which are at distance two from v in G. The first leap Zagreb index of a graph G is the sum of squares of the 2-degree of all vertices in G and the third leap Zagreb index of G is the sum of product of the degree and 2-degree of every vertex v in G. In this paper, we compute the first and third leap Zagreb indices of bridge and chain graphs. Also we apply these results to determine the first and third leap Zagreb indices of some chemical structures such as polyphenyl chains and spiro chains.

References

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