  We prove a sharp upper bound on the number of shortest cycles contained
inside any connected graph in terms of its number of vertices, girth, and
maximal degree. Equality holds only for Moore graphs, which gives a new
characterization of these graphs. In the case of regular graphs, our result
improves an inequality of Teo and Koh. We also show that a subsequence of the
Ramanujan graphs of Lubotzky-Phillips-Sarnak have super-linear kissing numbers.
