Some properties of zero-divisor graphs of direct products of finite fields

Abstract

This study investigates the zero-divisor graphs of the direct products of finite fields with vertex set consisting of non-zero zero divisors of the direct products of finite fields, and two distinct non-zero zero divisors are adjacent in the zero divisor graph if the product of the two distinct non-zero zero divisors is the additive identity of the direct products of finite fields. We prove that the metric chromatic number, clique number, vertex chromatic number are all equal to n, for the zero divisor graph of direct products of n finite fields, and also find the metric chromatic number, clique number, and vertex chromatic number of the complement graph of the zero-divisor graph of the direct product of n fields. The independence number, edge chromatic number, Eulerian and Hamiltonian properties of the zero-divisor graph and the complement graph are also determined.