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 λm 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 ξm = 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 λm ≤ ξm. The upper bound of λm is sharp.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Acta Mathematicae Applicatae Sinica, English Series
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
