Bounds on Elliptic Sombor and Euler Sombor indices of join and corona product of graphs

TL;DR

This paper establishes bounds for the Elliptic Sombor and Euler Sombor indices in join and corona graph products, showing these bounds are tight for regular graphs, thus advancing the understanding of these indices in graph theory.

Contribution

It provides the first bounds for these indices in join and corona products and characterizes when these bounds are achieved.

Findings

Bounds are derived for join and corona products.

Bounds are tight for regular graphs.

Provides formulas for specific graph classes.

Abstract

The Elliptic Somber and Euler Somber indices are newly defined topological indices based on the Somber index. Our paper presents calculations of the upper and lower bounds of these indices for the join and corona product of arbitrary graphs. Furthermore, we demonstrate that these bounds are attained when both graphs are regular.