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
On computing the connectivities of graphs and digraphs
β 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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π SIMILAR VOLUMES
## 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__ β€ Ο β€ Ξ΄ β 2, related with the number of short paths (in the case of graphs
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 ) .
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
## Abstract Let __G__β=β(__V__,__E__) be a graph or digraph and __r__ : __V__ β __Z__~+~. An __r__βdetachment of __G__ is a graph __H__ obtained by βsplittingβ each vertex Ξ½ β __V__ into __r__(Ξ½) vertices. The vertices Ξ½~1~,β¦,Ξ½~__r__(Ξ½)~ obtained by splitting Ξ½ are called the __pieces__ of Ξ½ in __H
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).