On the Elliptic Sombor and Euler Sombor indices of Corona product of certain graphs

TL;DR

This paper introduces and computes the elliptic Sombor and Euler Sombor indices for graphs formed by join and Corona product operations on standard graphs like paths, cycles, and complete graphs, expanding the understanding of these indices.

Contribution

It provides explicit formulas for the elliptic Sombor and Euler Sombor indices of graphs resulting from join and Corona product operations on common graph classes.

Findings

Derived formulas for elliptic Sombor indices of Corona products.

Derived formulas for Euler Sombor indices of join and Corona product graphs.

Extended the application of these indices to standard graph families.

Abstract

Elliptic Sombor and Euler Sombor indices are recently defined topological indices using Sombor index. Elliptic sombor index is defined as $ESO(G)=\sum_{uv\in E(G)}(d_u+ d_v)\sqrt{d^2_u+ d^2_v}$ and Euler Sombor index is defined as $EU(G)= \sum_{uv\in E(G)}\sqrt{{d_{u}^2+d_{v}^2}+d_ud_v}$, where $d_u$ and $d_v$ are degrees of vertices $u$ and $v$ in graph $G$. In this article, we compute the elliptic Sombor and Euler Sombor indices of some resultant graphs. Using the operations join and Corona product on standard graphs like path, cycle and complete graphs.