Dipartimento di Scienze di Base e Applicate per l'Ingegneria

Aula 1B1 (pal. 002)

Seminario di Geometria

Yue Zhou (Università di Napoli Federico II)

Abstract:

Let C(d,k) and AC(d,k) be the largest orders of a Cayley graph and a Cayley graph based on an abelian group, respectively, of degree d and diameter k. When k = 2, it is well-known that C(d,2) is at most d^2+1 with equality if and only if the graph is a Moore graph. In the abelian case, AC(d,2) is at most d^2/2 + d + 1. In this talk, we consider the construction of large graphs of diameter 2 using generalized difference sets. Our results improve the known lower bound on AC(d,2). This is a joint work with Alexander Pott.