Recently, Katre et al. introduced the concept of coprime index a graph. They asked to characterize graphs for which is same as clique number. In this paper, we partially solve problem. fact, prove that number and zero-divisor graph an ordered set ring Zpn coincide. Also, it proved annihilating ideal graphs, co-annihilating comaximal commutative rings can be realized specially constructed posets...

A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, 3, . . .,|V|} such that if an edge uv is assigned the label 1 if f(u) divides f(v) or f(v) divides f(u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial graph. ...

The Cartesian product of two hamiltonian graphs is always hamiltonian. For directed graphs, the analogous statement is false. We show that the Cartesian product C,,, x C,, of directed cycles is hamiltonian if and only if the greatest common divisor (g.c.d.) d of n, and n, is a t least two and there exist positive integers d,, d, so that d, + d, = d and g.c.d. (n,, d,) = g.c.d. (n,, d,) = 1. We ...