Kissing numbers of regular graphs (Q2095114)

The kissing number of a finite graph \(G\) is the number of distinct shortest oriented cycles in \(G\), in other words, the length of each cycle is the girth of the graph. The paper shows that graphs with large kissing numbers have large girth. The results provide a novel characterization of Moore graphs. In addition, the paper shows that the Ramanujan graphs of \textit{A. Lubotzky} et al. [Combinatorica 8, No. 3, 261--277 (1988; Zbl 0661.05035)] have super-linear kissing numbers. The paper is motivated by analogous results in topology, which is the source of the name kissing number.