Improved lower bound for the vertex connectivity of [formula omitted]-cages

Abstract

A ( δ , g ) -cage is a δ -regular graph with girth g and with the least possible number of vertices. We prove that all ( δ , g ) -cages are r-connected with r ⩾ δ + 1 for g ⩾ 7 odd. This result supports the conjecture of Fu, Huang and Rodger that all ( δ ; g ) -cages are δ -connected.