On the connectivity of cages with girth five, six and eight Original Research Article

A image-cage is a regular graph of degree image and girth g with the least possible number of vertices. Recently, some authors have addressed the problem of studying the connectivity of cages. In this direction, it was conjectured by Fu, Huang and Rodger that every image-cage is maximally connected, i.e., it is image-connected, and they proved this statement for image. We provide a new contribution to the proof of that conjecture, by showing that every image-cage with image is maximally connected, and by assuring either maximal connectivity or superconnectivity for some image-cages.