机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
Zhang, Zhao
[1
,2
]
Meng, Jixiang
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机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
Meng, Jixiang
[1
]
机构:
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
[2] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China
A graph G is said to be super-connected if any minimum cut of G isolates a vertex. In a previous work due to the second author of this note, super-connected graphs which are both vertex transitive and edge transitive are characterized. In this note, we generalize the characterization to edge transitive graphs which are not necessarily vertex transitive, showing that the only irreducible edge transitive graphs which are not super-connected are the cycles C-n (n >= 6) and the line graph of the 3-cube, where irreducible means the graph has no vertices with the same neighbor set. Furthermore, we give some sufficient conditions for reducible edge transitive graphs to be super-connected. (C) 2007 Elsevier B.V. All rights reserved.
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页码:1948 / 1953
页数:6
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[11]
Watkins M.E., 1970, Journal of Combinatorial Theory, V8, P23