- Title
- On superconnectivity of (4, g)-cages
- Creator
- Lu, Hongliang; Wu, Yunjian; Lin, Yuqing; Yu, Qinglin; Balbuena, Camino; Marcote, Xavier
- Relation
- Graphs and Combinatorics Vol. 29, Issue 1, p. 105-119
- Publisher Link
- http://dx.doi.org/10.1007/s00373-011-1091-5
- Publisher
- Springer Japan
- Resource Type
- journal article
- Date
- 2013
- Description
- A (k, g)-cage is a graph that has the least number of vertices among all k-regular graphs with girth g. It has been conjectured (Fu et al. in J. Graph Theory, 24:187-191, 1997) that all (k, g)-cages are k-connected for every k = 3. A k-connected graph G is called superconnected if every k-cutset S is the neighborhood of some vertex. Moreover, if G-S has precisely two components, then G is called tightly superconnected. In this paper, we prove that every (4, g)-cage is tightly superconnected when g = 11 is odd.
- Subject
- cage; superconnected; tightly superconnected
- Identifier
- http://hdl.handle.net/1959.13/1063484
- Identifier
- uon:17310
- Identifier
- ISSN:0911-0119
- Language
- eng
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