Line Graphs of Zero-Divisor Graphs of Finite Free Semilattices

Abstract

Let SLn be the finite free semilattice on xn={1,2,...,n} and Γn be the zero-divisor graph of SLn. Moreover, let L(Γn) be the line graph of Γn. In this paper, we find the cardinality of the vertex set of L(Γn), diameter, maximum degree, minimum degree, girth, clique number, chromatic number, and degrees of all vertices in L(Γn)for n≥3.