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Let D be an acyclic digraph. The competition graph of D has the same set of vertices as D and an edge between vertices u and v if and only if there is a vertex x in D such that (u, x) and (v, x) are arcs of D. In this paper, we show that the competition graphs of doubly partial orders are interval graphs. We also show that an interval graph together with(More)
The competition graph of a digraph was introduced by Cohen in 1968 associated with the study of ecosystems. Since then, the competition graph has been widely studied and many variations have been introduced. In this paper, we deÿne and study the m-step competition graph of a digraph which is another generalization of competition graph. ? 2000 Elsevier(More)
Let IB n be the set of all irreducible matrices in B n and let SIB n be the set of all symmetric matrices in IB n. Finding an upper bound for the set of indices of matrices in IBn and SIB n and determining gaps in the set of indices of matrices in IBn and SIBn has been studied by many researchers. In this paper, we establish a best upper bound for the set(More)
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