On the variable sum exdeg index and cut edges of graphs

Document Type : Original paper

Authors

1 Knowledge Unit of Science, University of Management and Technology, Sialkot, Pakistan

2 Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore (RCET), Pakistan

3 Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, UAE

4 Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il, Saudi Arabia

Abstract

The variable sum exdeg index of a graph $G$ is defined as $SEI_a(G)=\sum_{u\in V(G)}d_G(u)a^{d_G(u)}$, where $a\neq 1$ is a positive real number, $d_G(u)$ is the degree of a vertex $u\in V(G)$. In this paper, we characterize the graphs with the extremum variable sum exdeg index among all the graphs having a fixed number of vertices and cut edges, for every $a>1$.

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References

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Communications in Combinatorics and Optimization
Volume 6, Issue 2
December 2021
Pages 249-257

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