Aula 1B1 (pal. 002)
Seminario di Geometria
Yue Zhou (Università di Napoli Federico II)
Cayley graphs with diameter two from difference sets
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.