Zero-divisor graph of a poset with respect to an automorphism

In this paper, we introduce the zero-divisor graph of a poset with respect to an automorphism, called the generalized zero-divisor graph of a poset, as an extension of the zero-divisor graph of a poset. It is proved that for such graphs, the chromatic number and the clique number need not be equal. A sufficient condition is provided for the chromatic number and the clique number of the generalized zero-divisor graph to be equal, which extends the result of the zero-divisor graph of poset. Further, the connectedness, diameter and girth of such graphs are studied.