Macbeth, Heather; Šiagiová, Jana and Širáň, Jozef
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|DOI (Digital Object Identifier) Link:||http://dx.doi.org/10.1016/j.disc.2011.03.038|
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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)≤AC(d,2)≤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)≥(9/25)(d+3)(d−2) and AC(d,2)≥(3/8)(d2−4). We also offer a result for Cayley graphs of metacyclic groups for general degree and diameter.
|Item Type:||Journal Article|
|Copyright Holders:||2011 Elsevier B.V.|
|Keywords:||Cayley graph; degree-diameter problem; group; cyclic; Abelian; metacyclic|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics|
|Depositing User:||Jozef Širáň|
|Date Deposited:||09 Dec 2011 10:22|
|Last Modified:||03 Dec 2012 15:42|
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