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EDGE-CONNECTIVITIES OF GRAPHS AND DIGRAPHS

✍ Scribed by András Frank

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
216 KB
Volume
5
Category
Article
ISSN
1571-0653

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

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In this paper we give simple degree sequence conditions for the equality of edge-connectivity and minimum degree of a (di-)graph. One of the conditions implies results by Bollobás, Goldsmith and White, and Xu. Moreover, we give analogue conditions for bipartite (di-)graphs.

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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

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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 δ, maximum degree Δ, diameter __D__, and a new parameter l~pi;~, __0__ ≤ π ≤ δ − 2, related with the number of short paths (in the case of graphs