Sombor index of chemical graphs

Abstract

© 2021 Elsevier Inc. A graph G consists of a set of vertices V(G) and a set of edges E(G). Recently, a new vertex-degree-based molecular structure descriptor was introduced, defined as SO(G)=∑uv∈E(G)(du)2+(dv)2and named “Sombor index”. By du is denoted the degree of the vertex u∈V(G). In this paper we are concerned with the Sombor index of chemical graphs. Recall that G is a chemical graph if du≤4 for all u∈V(G). We characterize the graphs extremal with respect to the Sombor index over the following sets: (connected) chemical graphs, chemical trees, and hexagonal systems.