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 $SEI_a(G)=sum_{uin V(G)}d_G(u)a^{d_G(u)}$, where $aneq 1$ is a positive real number,  du(u) is the degree of a vertex u ∈ 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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