Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423527 | Discrete Mathematics | 2012 | 6 Pages |
Abstract
Let CC(d,2) and AC(d,2) be the largest order of a Cayley graph of a cyclic and an Abelian group, respectively, of diameter 2 and a given degree d. There is an obvious upper bound of the form CC(d,2)â¤AC(d,2)â¤d2/2+d+1. We prove a number of lower bounds on both quantities for certain infinite sequences of degrees d related to primes and prime powers, the best being CC(d,2)â¥(9/25)(d+3)(dâ2) and AC(d,2)â¥(3/8)(d2â4). We also offer a result for Cayley graphs of metacyclic groups for general degree and diameter.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Heather Macbeth, Jana Å iagiová, Jozef Å iráÅ,