The Euler Sombor Index and the Average Sombor Index of the Cozero-Divisor Graph over the Ring ℤn

Let Z(R)′ denote the set of all elements in the ring R that are neither zero nor units, where R is assumed to be a commutative ring with a multiplicative identity satisfying 1≠0. Two distinct vertices w and κ are defined to be adjacent if and only if κ does not lie in the ideal generated by w in R, that is, κ∉wR, and simultaneously, w does not lie in the ideal generated by κ in R, that is, w∉κR. The cozero-divisor graph of R, denoted by Γ′(R), is an undirected graph in which the vertices are given by the set Z(R)′. This article presents a comprehensive evaluation of both the Euler Sombor index and the average Sombor index for the graphs Γ′(Zn) corresponding to various values of n.