Sombor characteristic values of cographs

A unique class of cograph is examined, that is defined recursively as $C=C\left(n_1\right)={\bar{K}}_{n_1}$ , and $C=C(n_1,n_2,\dots ,n_i)=\overline{C(n_1,n_2,\dots ,n_{i-1})\cup K_{n_i}}$ , for $2\le i\le k$ . 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.