# Bounds on Sombor index and inverse sum indeg (ISI) index of graph operations

Document Type : Original paper

Authors

1 Department of Mathematical Sciences, College of Science, United Arab Emirate University, Al Ain 15551, Abu Dhabi, UAE

2 Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, United Arab Emirates

Abstract

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. Denote by $d_G(u)$ the degree of a vertex $u \in V(G)$. The Sombor index of $G$ is defined as $SO(G) = \sum_{uv \in E(G)} \sqrt{d_u^2 + d_v^2}$, whereas, the inverse sum indeg $(ISI)$ index is defined as $ISI(G) = \sum_{uv \in E(G)} \frac{d_{u}d_{v}}{d_{u} + d_{v}}.$ In this paper, we compute the bounds in terms of maximum degree, minimum degree, order and size of the original graphs $G$ and $H$ for Sombor and $ISI$ indices of several graph operations like corona product, cartesian product, strong product, composition and join of graphs.

Keywords

Main Subjects

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