Acta Mathematicae Applicatae Sinica, English Series

, Volume 19, Issue 3, pp 505–510 | Cite as

Bound on m-restricted Edge Connectivity

Original papers

Abstract

An m-restricted edge cut is an edge cut that separates a connected graph into a disconnected one with no components having order less than m. m-restricted edge connectivity λ m is the cardinality of a minimum m-restricted edge cut. Let G be a connected k-regular graph of order at least 2m that contains m-restricted edge cuts and X be a subgraph of G. Let ∂(X) denote the number of edges with one end in X and the other not in X and ξ m = min{∂(X) : X is a connected vertex-induced subgraph of order m}. It is proved in this paper that if G has girth at least m/2+ 2, then λ m ≤ ξ m . The upper bound of λ m is sharp.

Keywords

Regular graph bound restricted edge connectivity 

2000 MR Subject Classification

05C40 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsZhangzhou Normal CollegeFujianChina
  2. 2.Department ofMathematicsXiamen UniversityXiamenChina

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