Cayley Cages

  • Authors:

  • Geoffrey Exoo;Robert Jajcay;Jozef Širáň

  • Affiliations:

  • Department of Mathematics and Computer Science, Indiana State University, Terre Haute, USA 47809;Department of Mathematics and Computer Science, Indiana State University, Terre Haute, USA 47809;Department of Mathematics, SvF, Slovak University of Technology, Bratislava, Slovakia 813 68

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2013

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Abstract

A (k,g)-Cayley cage is a k-regular Cayley graph of girth g and smallest possible order. We present an explicit construction of (k,g)-Cayley graphs for all parameters k驴2 and g驴3 and generalize this construction to show that many well-known small k-regular graphs of girth g can be constructed in this way. We also establish connections between this construction and topological graph theory, and address the question of the order of (k,g)-Cayley cages.