New improvements on the connectivity of cages
Release Time:2025-04-30
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- Date:
- 2025-04-30
- Title of Paper:
- New improvements on the connectivity of cages
- Journal:
- Acta Mathematica Sinica
- Summary:
- A ( , g)-cage is a -regular graph with girth g and with the least possible number of
vertices. In this paper, we show that all ( , g)-cages with odd girth g 9 are r-connected, where
(r − 1)2 + p − 2 < r2 and all ( , g)-cages with even girth g 10 are r-connected, where r is the
largest integer satisfying r(r−1)2
4 + 1 + 2r(r − 1) . Those results support a conjecture of Fu, Huang
and Rodger that all ( , g)-cages are -connected.
- Co-author:
- H. Lu, Y. Wu, Q. L. Yu and Y. Lin
- Translation or Not:
- No
- Date of Publication:
- 2011-12-01