Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates; Corresponding author.
Bilal Ahmad Rather
Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates; Department of Applied Mathematics, School of Engineering, Samarkand International University of Technology, Samarkand 140100, Uzbekistan
Muhammad Imran
Department of Mathematical and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia
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.
