On dimension of some finite algebraic graphs of finite rings

Abstract

Suppose that ?? (Zp1p2···p? ) is a graph with the vertex set of nonzero zerodivisors of the finite ring Zp1p2...p? , where ? > 1, and x ? y is an edge if and only if x and y are ?-prime, where ? = {p1, p2, . . . , p?} is a set of odd prime numbers and a and b are ?-prime if either (a, b) = 1 or (a, b) = p, p /? ?. In this paper we study dimension, edge metric dimension and fraction dimension of the graph.