منابع مشابه
Distance connectivity in graphs and digraphs
Let G = (V, A) be a digraph with diameter D 6= 1. For a given integer 2 ≤ t ≤ D, the t-distance connectivity κ(t) of G is the minimum cardinality of an x → y separating set over all the pairs of vertices x, y which are at distance d(x, y) ≥ t. The t-distance edge connectivity λ(t) of G is defined similarly. The t-degree of G, δ(t), is the minimum among the out-degrees and in-degrees of all vert...
متن کاملOn connectivity of consecutive-d digraphs
The concept of a consecutive-d digraph was proposed by Du, Hsu and Hwang as a generalization of de Bruijn digraphs, Kautz digraphs, and their generalizations given by Imase and Itoh and Reddy, Pradhan and Kuhl. In this paper we determine the connectivity of consecutive-d digraphs and study how to modify consecutive-d digraphs to reach maximum connectivity. Our results will generalize and improv...
متن کاملRestricted Edge-Connectivity of de Bruijn Digraphs
The restricted edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks. This paper determines that the restricted edge-connectivity of the de Bruijn digraph B(d, n) is equal to 2d − 2 for d ≥ 2 and n ≥ 2 except B(2, 2). As consequences, the super edge-connectedness of B(d, n) is obtained immediately.
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The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability indices than the connectivity and the edge-connectivity. This paper shows that for a connected balanced digraph D and its line digraph L, if D is optimally super edge-connected, then κ1(L) = 2λ1(D), and that for a connected graph G and its line graph L, if one of κ1(L) and λ2(G) exists, then κ1...
متن کاملConnectivity of some Algebraically Defined Digraphs
Let p be a prime, e a positive integer, q = pe, and let Fq denote the finite field of q elements. Let fi : Fq → Fq be arbitrary functions, where 1 6 i 6 l, i and l are integers. The digraph D = D(q; f), where f = (f1, . . . , fl) : Fq → Fq, is defined as follows. The vertex set of D is Fl+1 q . There is an arc from a vertex x = (x1, . . . , xl+1) to a vertex y = (y1, . . . , yl+1) if xi + yi = ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1973
ISSN: 0095-8956
DOI: 10.1016/0095-8956(73)90018-x