Diameter 2 Cayley Graphs of Dihedral Groups

Grahame Erskine

doi:10.1016/j.disc.2015.01.023

paper

Diameter 2 Cayley Graphs of Dihedral Groups

arXiv:1403.4741 · doi:10.1016/j.disc.2015.01.023

Abstract

We consider the degree-diameter problem for Cayley graphs of dihedral groups. We find upper and lower bounds on the maximum number of vertices of such a graph with diameter 2 and degree $d$ . We completely determine the asymptotic behaviour of this class of graphs by showing that both limits are asymptotically $d^{2} /2$ .

5 pages; amended to expand remarks