Sombor Index and Sombor Spectrum of Cozero-Divisor Graph of $\mathbb Z_n$

Abstract

Let $\mathscr {Z}(\mathscr {R})'$ be the set of all non-unit and non-zero elements of ring $\mathscr {R}$, a commutative ring with identity $1\ne 0$. The cozero-divisor graph of $\mathscr {R}$, denoted by the notation ${\Gamma '(\mathscr {R})}$, is an undirected graph with vertex set $\mathscr {Z}(\mathscr {R})'$. Any two distinct vertices w and z are adjacent if and only if $w\notin z\mathscr {R}$ and $z\notin w\mathscr {R}$, where $q\mathscr {R}$ is the ideal generated by the element q in $\mathscr {R}$. In this article, we evaluate the Sombor index of the graphs ${\Gamma '(\mathbb Z_n)}$ for different values of n. Additionally, we compute ${\Gamma '(\mathbb Z_{n})}$, the cozero-divisor graph Sombor spectrum.