On Superconnectivity of (4, g)-Cages
Release Time:2025-04-30
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- Date:
- 2025-04-30
- Title of Paper:
- On Superconnectivity of (4, g)-Cages
- Journal:
- Graph and Combinatorics
- Summary:
- 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.
- Co-author:
- Hongliang Lu.et.al
- Volume:
- 2013, Volume 29, Issue 1
- Page Number:
- 105-119
- Translation or Not:
- No
- Date of Publication:
- 2013-12-31