Let (P,≤) be a partially ordered set with a least element 0. The regular digraph of ideals of P, denoted by \gama (P), is a digraph whose vertex-set is the set of all nontrivial ideals of P and, for every two distinct vertices I and J , there is an arc from I to J whenever I contains a nonzero zero-divisor on J . Also, the undirected regular graph of ideals of P, denoted by \gama(P), is a graph with all nontrivial ideals of P being the vertex-set, and for two distinct vertices I and J , I is adjacent to J if and only if I contains a nonzero zero-divisor on J or J contains a nonzero zero-divisor on I . In this paper, we study some basic properties of \gama (P). Also we completely characterize all posets P with planar regular graph.

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