Comments on the Clique Number of Zero-Divisor Graphs of Zn

Abstract

In 2008, J. Skowronek-kazio´w extended the study of the clique number ωGZn to the zero-divisor graph of the ring Zn, but their result was imperfect. In this paper, we reconsider ωGZn of the ring Zn and give some counterexamples. We propose a constructive method for calculating ωGZn and give an algorithm for calculating the clique number of zero-divisor graph. Furthermore, we consider the case of the ternary zero-divisor and give the generation algorithm of the ternary zero-divisor graphs.