On the cozero-divisor graphs associated to rings

Abstract

Let R be a ring with unity. The cozero-divisor graph of a ring R, denoted by is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of R, and two distinct vertices x and y are adjacent if and only if and In this paper, first we study the Laplacian spectrum of We show that the graph is Laplacian integral. Further, we obtain the Laplacian spectrum of for where and p, q are distinct primes. In order to study the Laplacian spectral radius and algebraic connectivity of we characterized the values of n for which the Laplacian spectral radius is equal to the order of Moreover, the values of n for which the algebraic connectivity and vertex connectivity of coincide are also described. At the final part of this paper, we obtain the Wiener index of for arbitrary n.