The minimum number of vertices with girth 6 and degree set D = {r,m}
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 249-258 |
| Journal / Publication | Discrete Mathematics |
| Volume | 269 |
| Issue number | 1-3 |
| Publication status | Published - 28 Jul 2003 |
| Externally published | Yes |
Link(s)
Abstract
A (D;g)-cage is a graph having the minimum number of vertices, with degree set D and girth g. Denote by f(D;g) the number of vertices in a (D;g)-cage. In this paper it is shown that f({r,m};6)≥2(rm-m+1) for any 2≤r<m, and f({r,m};6)=2(rm-m+1) if either (i) 2≤r≤5 and r<m or (ii) m-1 is a prime power and 2≤r<m. Upon these results, it is conjectured that f({r,m};6)=2(rm-m+1) for any r with 2≤r<m. © 2002 Elsevier B.V. All rights reserved.
Research Area(s)
- Cage, Degree set, Girth, Symmetric graph
Bibliographic Note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to lbscholars@cityu.edu.hk.
Citation Format(s)
The minimum number of vertices with girth 6 and degree set D = {r,m}. / Yuansheng, Yang; Liang, Weifa.
In: Discrete Mathematics, Vol. 269, No. 1-3, 28.07.2003, p. 249-258.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
