Large "De Bruijn" Cayley graphs and digraphs (original) (raw)

We present families of undirected and directed Cayley graphs whose construction is motivated by that of the De Bruijn graphs. One approach yields, for every large k and for values of d taken from a large interval, the largest known Cayley graphs and digraphs of diameter k and degree d. Another method yields, for every k 3 and infinitely many values of d, Cayley graphs and digraphs of diameter k and degree d whose order is exponentially larger in k than any previously constructed. In the directed case, these are within a polynomial factor of the Moore bound.