More on Sombor Index of Graphs

Abstract

Recently, a novel degree-based molecular structure descriptor, called Sombor index was introduced. Let G=(V(G),E(G)) be a graph. Then, the Sombor index of G is defined as SO(G)=∑uv∈E(G)dG2(u)+dG2(v). In this paper, we give some lemmas that can be used to compare the Sombor indices between two graphs. With these lemmas, we determine the graph with maximum SO among all cacti with n vertices and k cut edges. Furthermore, the unique graph with maximum SO among all cacti with n vertices and p pendant vertices is characterized. In addition, we find the extremal graphs with respect to SO among all quasi-unicyclic graphs.

Keywords

• topological index
• vertex degree
• Sombor index
• cactus
• quasi-unicyclic graph