The p-Competition Graphs of Symmetric Digraphs and p-Neighborhood Graphs
نویسندگان
چکیده
The p-competition graph G of a digraph D is a graph on the same vertex set as D, with x; y] 2 E(G) if and only if jOut(x) \Out(y)j p in D. In this paper we focus on the case in which D is a symmetric digraph ((a; b) is an arc in D if and only if (b; a) is an arc in D). We relate the problem to 2-step graphs, squares, and a generalization of the neighborhood graph called the p-neighborhood graph. We also identify some familiar classes of graphs as 2-competition graphs of loopless symmetric digraphs.
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