Degree-based topological indices of the idempotent graph of the ring Zn

Abstract

Let $R$ be a finite commutative ring with a non-zero identity, and $Id\left(R\right)$ be the set of idempotent elements of $R$. The idempotent graph of $R$, denoted by $G_{Id}\left(R\right)$, is a simple undirected graph with all elements of $R$ as vertices, and two distinct vertices $u$, $v$ are adjacent if and only if $u+v\in Id\left(R\right)$. In this paper, we consider the idempotent graph of the ring $Z_n$ and investigate some degree-based topological indices, such as the general sum-connectivity index, the general Randić index, the general Zagreb index, and the Sombor index of that graph by considering the $M$-polynomial of the graph.