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

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