Sombor characteristic values of cographs

Abstract

A unique class of cograph is examined, that is defined recursively as C=C(n1)=K‾n1, and C=C(n1,n2,…,ni)=C(n1,n2,…,ni−1)∪Kni‾, for 2≤i≤k. The Sombor spectrum of C is calculated, the Sombor spectral radius and establish the sharp bounds for the Sombor index, and the greatest and smallest Sombor characteristic values. We present results on the Sombor energy of cographs and identify the graphs that reach the inequalities. Also, we characterize cographs with simple Sombor characteristic values and cographs with unique characteristic values.

Keywords

• Sombor matrix
• Sombor index
• Cographs graphs
• Characteristic values