The Zero-Divisor Graph of a Meet-Semilattice

Abstract

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