The super spanning connectivity of arrangement graph

A \(k\)-container \(C(u, v)\) of a graph \(G\) is a set of \(k\) internally disjoint paths between \(u\) and \(v\). A \(k\)-container \(C(u, v)\) of \(G\) is a \(k^*\)-container if it is a spanning subgraph of \(G\). A graph \(G\) is \(k^*\)-connected if there exists a \(k^*\)-container between any...

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Bibliographic Details
Published inarXiv.org
Main Authors Li, Pingshan, Xu, Min
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 16.06.2016
Subjects
Apexes
Containers
Graph theory
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Summary:A \(k\)-container \(C(u, v)\) of a graph \(G\) is a set of \(k\) internally disjoint paths between \(u\) and \(v\). A \(k\)-container \(C(u, v)\) of \(G\) is a \(k^*\)-container if it is a spanning subgraph of \(G\). A graph \(G\) is \(k^*\)-connected if there exists a \(k^*\)-container between any two different vertices of G. A \(k\)-regular graph \(G\) is super spanning connected if \(G\) is \(i^*\)-container for all \(1\le i\le k\). In this paper, we prove that the arrangement graph \(A_{n, k}\) is super spanning connected if \(n\ge 4\) and \(n-k\ge 2\).
ISSN:2331-8422