منابع مشابه
Distance Sequences In Locally Infinite Vertex-Transitive Digraphs
We prove that the out-distance sequence {f(k)} of a vertex-transitive digraph of finite or infinite degree satisfies f(k + 1) ≤ f(k) for k ≥ 1, where f(k) denotes the number of vertices at directed distance k from a given vertex. As a corollary, we prove that for a connected vertextransitive undirected graph of infinite degree d, we have f(k) = d for all k, 1 ≤ k < diam(G). This answers a quest...
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Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is 3-transitive if the existence of the directed path (u, v, w, x) of length 3 in D implies the existence of the arc (u, x) ∈ A(D). In this article strong 3-transitive digraphs are characterized and the structure of non-strong 3-transitive digraphs is described. The results are used, e.g...
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Let D = (V , A) be a directed graph (digraph) without loops nor multiple arcs. A set of vertices S of a digraph D is a (k, l)-kernel of D if and only if for any two vertices u, v in S, d(u, v) ≥ k and for any vertex u in V \ S there exists v in S such that d(u, v) ≤ l. A digraph D is called quasi-transitive if and only if for any distinct vertices u, v, w of D such that u→ v → w, then u and w a...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1980
ISSN: 0012-365X
DOI: 10.1016/0012-365x(80)90155-7