G-graphs for the cage problem: a new upper bound

Constructing some regular graph with a given girth, a given degree and the fewest possible vertices is a hard problem. This problem is called the cage graph problem and has some links with the error codes theory. In this paper we presents some new graphs, constructed from a group, with a girth of 6 and regular of degree p, for any prime number p. This graphs are of order 2×p2 when the best upper bound known for the (p, 6)-cage problem was the Sauer bound, equal to 4(p − 1)3 . Categories and Subject Descriptors G.2.2 [Discrete Mathematics]: Graph Theory—Graph algorithms General Terms Algorithms, Theory Keywords Cage graphs, graphs from group, G-graphs.

• Type: Conference
• Year: 2007
• Where: ISSAC
• Authors: Alain Bretto, Luc Gillibert
• Keywords: Cage Graph Problem, Cage Graphs, Fewest Possible Vertices, ISSAC 2007