## Abstract Let __G__ be a connected graph of order __p__ ≥ 2, with edge‐connectivity κ~1~(__G__) and minimum degree δ(__G__). It is shown her ethat in order to obtain the equality κ~1~(__G__) = δ(__G__), it is sufficient that, for each vertex __x__ of minimum degree in __G__, the vertices in the n
Sufficient conditions for equality of connectivity and minimum degree of a graph
✍ Scribed by Jerzy Topp; Lutz Volkmann
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 270 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
For a graph G, let n(G), κ(G) and δ(G) denote the order, the connectivity, and the minimum degree of G, respectively. The paper contains some conditions on G implying κ(G) = δ(G). One of the conditions is that n(G) ≤ δ(G)(2__p__ −1)/(2__p__ −3) if G is a p‐partite graph. © 1993 John Wiley & Sons, Inc.
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