A lower bound on the order of regular graphs with given girth pair
- Authors: Balbuena, Camino , Jiang, T. , Lin, Yuqing , Marcote, Xavier , Miller, Mirka
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of Graph Theory Vol. 55, no. 2 (2007), p. 153-163
- Full Text: false
- Reviewed:
- Description: The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair was proved by Harary and Kovács [Regular graphs with given girth pair, J Graph Theory 7 (1983), 209-218]. A (
- Description: C1
- Description: 2003004727
All (k;g)-cages are k-edge-connected
- Authors: Lin, Yuqing , Miller, Mirka , Rodger, Chris
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Graph Theory Vol. 48, no. 3 (2005), p. 219-227
- Full Text: false
- Reviewed:
- Description: A (k;g)-cage is a k-regular graph with girth g and with the least possible number of vertices. In this paper, we prove that (k;g)-cages are k-edge-connected if g is even. Earlier, Wang, Xu, and Wang proved that (k;g)-cages are k-edge-connected if g is odd. Combining our results, we conclude that the (k;g)-cages are k-edge-connected. © 2005 wiley Periodicals, Inc.
- Description: C1