Interval p-Neighborhood Graphs
نویسندگان
چکیده
The (p)-neighborhood graph of a graph G, denoted N p (G), is de-ned on the same vertex set as G, with x; y] 2 E (N 2 (G)) if and only if jN(x)\N(y)j p in G, where N (v) is the open neighborhood of vertex v. The p]-neighborhood graph of G, N p G], is deened similarly, using closed neighborhoods rather than open ones. If G is the underlying graph of a symmetric digraph D, then the p-neighborhood graph of G is the p-competition graph of D. The case p = 1 has been studied by several authors. We consider the general case, asking, \which graphs have interval p-neighborhood graphs", and give speciic results for the case p = 2.
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