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

Abstract

Graph theory has wide-ranging applications in chemistry, nano science and networking problems. The corona product operation effec tively represents compounds like dendrimers, where a central molecule is encircled by multiple repeating units. By representing atoms as vertices and bonds as edges, graph theory provides a clear and structured way to analyze and understand the architecture of intricate chemical compounds through various graph operations. The corona product of two graphs G and H gives a new graph obtained by taking one copy of G and |V (G)| copies of H by joining ith vertex of G to every ith copy of H. Elliptic Sombor and Euler Sombor indices are recently defined topo logical indices using Sombor index. Elliptic sombor index is defined as ESO(G) = uv∈E(G)(du +dv) d2 u +d2 v and Euler Sombor index is defined as EU(G) = uv∈E(G) d2 u + d2 v + dudv, where du and dv are degrees of vertices u and v in graph G. In this article, we compute the Elliptic Sombor and Euler Sombor indices of few resultant graphs using the operations join and corona product on standard graphs like path, cycle and complete graphs.