Large Cayley graphs and vertex‐transitive non‐Cayley graphs of given degree and diameter

Abstract

Abstract For any d ⩾5 and k ⩾3 we construct a family of Cayley graphs of degree d , diameter k , and order at least k (( d −3)/3) k . By comparison with other available results in this area we show that our family gives the largest currently known Cayley graphs for a wide range of sufficiently large degrees and diameters. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 87–98, 2010