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.