KG-SOMBOR ENERGY OF GRAPHS WITH SELF LOOPS.

Let G = (V, E) be a connected graph. A topological invariant named KG-Sombor index was introduced by V. R. Kulli, defined as KG = KG(G) = ∑_ue√ d(u) ² + d(e) ², where ∑ _ue indicates summation over vertices u ∈ V (G) and the edges e ∈ E(G) that are incident to u. In this paper, we extend the KG-Sombor index of simple graphs to graph with self loops. We study some properties of KG-Sombor eigenvalues and few bounds for KG-Sombor energy of graphs with self loops and KG-Sombor characteristic polynomial of graphs with self loops. [ABSTRACT FROM AUTHOR]