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June 2020 On the reduced second Zagreb index of graphs
Fang Gao, Kexiang Xu
Rocky Mountain J. Math. 50(3): 975-988 (June 2020). DOI: 10.1216/rmj.2020.50.975

Abstract

For a connected graph G, the reduced second Zagreb index is defined as

R M 2 = R M 2 ( G ) = u v E ( G ) ( d G ( u ) 1 ) ( d G ( v ) 1 ) ,

where dG(u) and dG(v) denote the degrees of vertices u and v in graph G, respectively. We determine the extremal graphs among all connected graphs of order n and with n2m edges with respect to RM2, and obtain the first ten largest RM2 for connected graphs of order n. Moreover, we characterize the sharp upper bound on RM2 for all connected bipartite graphs with given connectivity k. Finally, the extremal graphs with respect to RM2 are determined in all connected bipartite graphs with matching number q.

Citation

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Fang Gao. Kexiang Xu. "On the reduced second Zagreb index of graphs." Rocky Mountain J. Math. 50 (3) 975 - 988, June 2020. https://doi.org/10.1216/rmj.2020.50.975

Information

Received: 14 January 2020; Accepted: 15 December 2019; Published: June 2020
First available in Project Euclid: 29 July 2020

zbMATH: 07235591
MathSciNet: MR4132621
Digital Object Identifier: 10.1216/rmj.2020.50.975

Subjects:
Primary: 05C12, 05C35

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 3 • June 2020
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