The m-step competition graph G of a digraph D with the same vertex set as D,satisfying that the verticesxand y in G are adjacent,if and only if there is a vertex a and two directed paths with length m from x to a and from y to a in D.For an undirected graph G,the union of G and some isolated vertices is an m-step competition graph of an acyclic digraph.The minimum number of isolated vertices added is called the m-step competition number of G.This paper mainly studied the m≥1-step competition number of cactus graphs.
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