More on KG-Sombor Index of Graphs

Abstract

Topological indices are generally graph-invariant numerical properties that describe the topology of a graph. The KG-Sombor index, a vertex-edge version of the Sombor index, was recently defined as follows: $KG(G)=\sum\limits_{ue} \sqrt{d(u)^2+d(e)^2},$ where $\sum\limits_{ue}$
indicates summation over vertices $u \in V(G)$ and the edges $e \in E(G)$ that are incident to $u$. In this work, we obtained the effect of vertex and edge removal on KG-Sombor index. Also, characterized integer values of KG-Sombor index. Finally, computed a bound for the KG Sombor index of derived graphs, including the join of graphs, the m-splitting graph, the m-shadow graph, and the corona product of graphs.