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On computing the connectivities of graphs and digraphs

✍ Scribed by Abdol H. Esfahanian; S. Louis Hakimi


Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
670 KB
Volume
14
Category
Article
ISSN
0028-3045

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πŸ“œ SIMILAR VOLUMES


On the distance connectivity of graphs a
✍ M.A. Fiol; J. FΓ brega πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 475 KB

Let G=( V, E) be a digraph with diameter D # 1. For a given integer 1 t. The t-distance edge-connectivity of G is defined analogously. This paper studies some results on the distance connectivities of digraphs and bipartite digraphs. These results are given in terms of the parameter I, which can be

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## Abstract This paper studies the relation between the connectivity and other parameters of a digraph (or graph), namely its order __n__, minimum degree Ξ΄, maximum degree Ξ”, diameter __D__, and a new parameter l~pi;~, __0__ ≀ Ο€ ≀ Ξ΄ βˆ’ 2, related with the number of short paths (in the case of graphs

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Recently, it was proved that if the diameter D of a graph G is small enough in comparison with its girth, then G is maximally connected and that a similar result also holds for digraphs. More precisely, if the diameter D of a digraph G satisfies D 5 21 -1, then G has maximum connectivity ( K = 6 ) .

Distance connectivity in graphs and digr
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Let G = ( V , A ) be a digraph with diameter D # 1. For a given integer 2 5 t 5 D , the t-distance connectivity K ( t ) of G is the minimum cardinality of an z --+ y separating set over all the pairs of vertices z, y which are a t distance d(z, y) 2 t. The t-distance edge connectivity X ( t ) of G i

Highly edge-connected detachments of gra
✍ Alex R. Berg; Bill Jackson; Tibor JordΓ‘n πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 107 KB

## Abstract Let __G__ = (__V__,__E__) be a graph or digraph and __r__ : __V__ β†’ __Z__~+~. An __r__‐detachment of __G__ is a graph __H__ obtained by β€˜splitting’ each vertex Ξ½ ∈ __V__ into __r__(Ξ½) vertices. The vertices Ξ½~1~,…,Ξ½~__r__(Ξ½)~ obtained by splitting Ξ½ are called the __pieces__ of Ξ½ in __H

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✍ Jiping Liu; ; Huishan Zhou πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 230 KB

In this paper, we show that for any given two positive integers g and k with g > 3, there exists a graph (digraph) G with girth g and connectivity k. Applying this result, we give a negative answer to the problem proposed by M. Junger, G. Reinelt and W.R Pulleyblank (1985).