The Zero-Divisor Graph of a Meet-Semilattice

Abstract

In this paper, we introduce the zero-divisor graph \(\Gamma(L)\) of a meet-semilattice \(L\) with 0. It is shown that \(\Gamma(L)\) is connected with \(\text{diam}(\Gamma(L)) \leq 3\) and if \(\Gamma(L)\) contains a cycle, then the core \(K\) of \(\Gamma(L)\) is a union of 3-cycles and 4-cycles.