On Some Properties of Cages

Tao Wang1, Baogang Xu2, Qinglin Yu3
1School of Mathematics and Information Sciences Henan University, Kaifeng, China
2School of Mathematics and Computer Science Nanjing Normal University, Nanjing, China
3Department of Mathematics and Statistics Thompson Rivers University, Kamloops, BC, Canada

Abstract

A \((k;g)\)-cage is a graph with the minimum order among all \(k\)-regular graphs with girth \(g\). As a special family of graphs, \((k;g)\)-cages have a number of interesting properties. In this paper, we investigate various properties of cages, e.g., connectivity, the density of shortest cycles, bricks and braces.