Abstract | ||
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Let X = (V, E) be a connected vertex-transitive graph with degree k. Call X super restricted edge-connected, in short, sup-lambda', if F is a minimum edge set of X such that X - F is disconnected and every component of X - F has at least two vertices, then F is the set of edges adjacent to a certain edge in X. Wang [Y, Q, Wang, Super restricted edge-connectivity of vertex-transitive graphs, Discrete Mathematics 289 (2004) 199-205] proved that a connected vertex-transitive graph with degree k > 2 and girth g > 4 is sup-lambda'. In this paper, by studying the lambda'-superatom of X, we present sufficient and necessary conditions for connected vertex-transitive graphs and Cayley graphs with degree k > 2 to be sup-lambda'. In particular, sup-lambda' connected vertex-transitive graphs with degree k > 2 and girth g > 3 are completely characterized. These results can be seen as an improvement of the one which is obtained by Wang. |
Year | Venue | Keywords |
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2014 | ARS COMBINATORIA | Vertex-transitive graph,Restricted edge-connectivity,lambda'-optimal,Super restricted edge-connectivity,Cayley graph |
Field | DocType | Volume |
Discrete mathematics,Graph,Combinatorics,Vertex (geometry),Mathematics,Transitive relation | Journal | 113 |
ISSN | Citations | PageRank |
0381-7032 | 0 | 0.34 |
References | Authors | |
0 | 2 |
Name | Order | Citations | PageRank |
---|---|---|---|
Yingzhi Tian | 1 | 20 | 9.28 |
Jixiang Meng | 2 | 353 | 55.62 |