Spectral Analysis and Topological Indices of Cozero-Divisor Graphs over Commutative Rings

Let 1≠0 be the identity of the commutative ring R. The cozero-divisor graph of a ring R is an undirected simple graph, represented by Γ′(R), where two different vertices g and h are adjacent if and only if g∉Rh and h∉Rg. The vertices of this graph are given by the set of all non-zero and non-unit elements of R. The definition of a graph G’s Aα matrix is Aα(G)=αD(G)+(1−α)A(G), where α∈[0,1],D(G)=diag(deg(c1),deg(c2),…,deg(cn)) is the diagonal matrix and A(G) is the adjacency matrix of graph G. In this article, we calculate the sum-connectivity F-index, product-connectivity F-index of Γ′(Zn), when n=ζ1ζ2,ζ12ζ2,ζ1ζ2ζ3, and the Aα eigenvalues of Γ′(Zn) for n=ζ1u1ζ2ζ3, where ζ1,ζ2, ζ3 are distinct primes.