Large circulant graphs of fixed diameter and arbitrary degree

David Bevan, Grahame Erskine, Robert Lewis

Research output: Contribution to journalArticle

Abstract

We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a given diameter have concentrated mainly on the diameter 2 case. We present a direct product construction yielding improved bounds for small diameters and introduce a new general technique for “stitching” together circulant graphs which enables us to improve the current best known asymptotic orders for every diameter. As an application, we use our constructions in the directed case to obtain upper bounds on the minimum size of a subset A of a cyclic group of order n such that the k-fold sumset kA is equal to the whole group. We also present a revised table of largest known circulant graphs of small degree and diameter.
LanguageEnglish
Pages275–291
Number of pages17
JournalArs Mathematica Contemporanea
Volume13
Issue number2
Early online date9 Mar 2017
StateE-pub ahead of print - 9 Mar 2017

Fingerprint

Circulant Graph
Directed graphs
Arbitrary
Sumsets
Stitching
Direct Product
Cyclic group
Directed Graph
Table
Fold
Upper bound
Subset

Keywords

  • degree-diameter problem
  • sumsets
  • circulant graphs
  • Cayley graphs

Cite this

Bevan, David ; Erskine, Grahame ; Lewis, Robert. / Large circulant graphs of fixed diameter and arbitrary degree. In: Ars Mathematica Contemporanea. 2017 ; Vol. 13, No. 2. pp. 275–291
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Large circulant graphs of fixed diameter and arbitrary degree. / Bevan, David; Erskine, Grahame; Lewis, Robert.

In: Ars Mathematica Contemporanea, Vol. 13, No. 2, 09.03.2017, p. 275–291.

Research output: Contribution to journalArticle

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