Generalized competition index of a primitive digraph
نویسندگان
چکیده
منابع مشابه
The double competition multigraph of a digraph
The competition graph of a digraph is defined to be the intersection graph of the family of the out-neighborhoods of the vertices of the digraph (see [6] for intersection graphs). A digraph D is a pair (V (D), A(D)) of a set V (D) of vertices and a set A(D) of ordered pairs of vertices, called arcs. An arc of the form (v, v) is called a loop. For a vertex x in a digraph D, we denote the out-nei...
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The competit ion graph of a digraph was first defined in 1968 by Cohen in the study of ecosystems. The competition graph essentially relates any two species which have a common prey. In this paper, a compet i t ion-common enemy graph of a digraph is defined and studied. As the term suggests, it relates any two species which have a common prey and a common enemy. Results analogous to those found...
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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 de ne and study the m-step competition graph of a digraph which is another generalization of competition graph. ? 2000 Elsevier Science B.V. All rights reserved.
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Abstract. For positive integers m and n with 1 ≤ m ≤ n, the m-competition index (generalized competition index) of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y in D, there exist m distinct vertices v1, v2, . . . , vm such that there exist walks of length k from x to vi and from y to vi for each i = 1, . . . , m. In this paper, ...
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We study endomorphisms of a free group of finite rank by means of their action on specific sets of elements. In particular, we prove that every endomorphism of the free group of rank 2 which preserves an automorphic orbit (i.e., acts “like an automorphism” on one particular orbit), is itself an automorphism. Then, we consider elements of a different nature, defined by means of homological prope...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.01.033