Relations between elliptic Sombor index and some known topological indices

For a graph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text], the elliptic Sombor index [Formula: see text] is defined as [Formula: see text] where [Formula: see text] is the degree of the vertex [Formula: see text]. In this paper, we obtain sharp bounds on the elliptic Sombor index in terms of some graph parameters and other topological indices. Furthermore, we analyze star graphs [Formula: see text] to demonstrate how the established bounds behave in the context of highly irregular graphs.