In this paper, we introduce the Cayley graph of a partially ordered set (poset). Let (P, ≤) be a poset, and let S be a subset of P. We define the undirected Cayley graph of P, denoted by Cay(P, S), as a graph with vertex-set P and edge-set E consisting of those sets {x, y} such that y {x, s} ~? or x {y, s}~? for some s S, where for a subset T of P, T~? is the set of all x P such that x ≤ t, for all t T. We study some basic properties of Cay(P, S) such as connectivity, diameter and girth.
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