Zero-divisor graphs of Catalan monoid

Let C-n be the Catalan monoid on X-n = {1, , n} under its natural order. In this paper, we describe the sets of left zero-divisors, right zero-divisors and two sided zero-divisors of C-n; and their numbers. For n >= 4, we define an undirected graph Gamma(C-n) associated with C-n whose vertices are the two sided zero-divisors of C-n excluding the zero element theta of C-n with distinct two vertices alpha and beta joined by an edge in case alpha beta = theta = beta alpha. Then we first prove that Gamma(C-n) is a connected graph, and then we find the diameter, radius, girth, domination number, clique number and chromatic numbers and the degrees of all vertices of Gamma(C-n). Moreover, we prove that Gamma(C-n) is a chordal graph, and so a perfect graph.