In this paper, we study basic properties such as connectivity, diameter and girth of the zero-divisor graph Γ(Mn(L)) of n × n matrices over a lattice L with 0. Further, we consider the zero-divisor graph Γ(M2(Cn)) of 2 × 2 matrices over an n-element chain Cn. We determine the number of vertices, degree of each vertex, domination number and edge chromatic number of Γ(M2(Cn)). Also, we show that Beck’s Conjecture is true for Γ(M2(Cn)). Further, we prove that Γ(M2(Cn)) is hyper-triangulated graph.
['Anagha Khiste', 'Vinayak Joshi']
Zero-divisor graphs of matrices over lattices