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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Published in | arXiv.org |
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Main Authors | , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
16.06.2016
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Subjects | |
Online Access | Get full text |
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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 \(n-k\ge 2\). |
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ISSN: | 2331-8422 |