Abstract
For a graph \(G\) with \(V(G)=\{v_{1},v_{2},\dots, v_{n}\}\) and degree sequence \((d_{v_{1}},d_{v_{2}},\dots,d_{v_{n}})\), the adjacency matrix \(A(G)\) of \(G\) is a \((0,1)\) square matrix of order \(n\) with \(ij\)-th entry 1, if \(v_{i}\) is adjacent
to \(v_{j}\) and 0, otherwise. The Sombor matrix \(S(G)=(s_{ij})\) is a square matrix of order \(n\), where \(s_{ij}=\sqrt{d_{v_{i}}^{2}+d_{v_{j}}^{2}}\), whenever \(v_{i}\) is adjacent to \(v_{j}\), and 0, otherwise. The sum of the absolute
values of the eigenvalues of \(A(G)\) is the energy, while the sum of the absolute eigenvalues of \(S(G)\) is the Sombor energy of \(G\). In this note, we provide counter examples to the upper bound of Theorem 18 in [13] and Theorem 1
in [16].
