Small vertex-transitive and Cayley graphs of girth six and given degree: an algebraic approach

  • Authors:

  • Eyal Loz;Martin Mačaj;Mirka Miller;Jana Šiagiová;Jozef Širáň;Jana Tomanová

  • Affiliations:

  • University of auckland auckland, New Zealand;Comenius university bratislava, Slovakia;The university of newcastle newcastle, Australia and University of west bohemia pilsen, Czech Republic and Kings college, London, United Kingdom and Itb bandung, Indonesia;Slovak university of technology bratislava, Slovakia;Slovak university of technology bratislava, Slovakia and Open university, Milton Keynes, United Kingdom;Comenius university bratislava, Slovakia

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2011

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Abstract

We examine the existing constructions of the smallest known vertex-transitive graphs of a given degree and girth 6. It turns out that most of these graphs can be described in terms of regular lifts of suitable quotient graphs. A further outcome of our analysis is a precise identification of which of these graphs are Cayley. We also investigate higher level of transitivity of the smallest known vertex-transitive graphs of a given degree and girth 6 and relate their constructions to near-difference sets. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:265-284, 2011 © 2011 Wiley Periodicals, Inc.