Sombor index and elliptic Sombor index of benzenoid systems

Abstract

Let G be a graph with vertex set V and edge set E. A topological index has the formTI(G)=∑uv∈Ef(du,dv), where f=f(x,y) is a pertinently chosen function which must be symmetric and real-valued for all x,y pertaining to vertex degrees of the graph G. Particularly interesting are the Sombor index SO and the elliptic Sombor index ESO, induced by the functions f(x,y)=x2+y2 and f(x,y)=(x+y)x2+y2, respectively. In this paper we analyze the ordering relations in benzenoid systems with respect to these two important topological indices. Also, we extend the results to general Sombor index SOα,β and general elliptic Sombor index ESOα.