Hamiltonian connectivity of 2-tree-generated networks

In this paper we consider a class of Cayley graphs that are generated by certain 3-cycles on the alternating group A n . These graphs are generalizations of the alternating group graph A G n . We look at the case when the 3-cycles form a “tree-like structure”, and analyze the Hamiltonian connectivity of such graphs. We prove that even with 2 n − 7 vertices deleted, the remaining graph is Hamiltonian connected, i.e. there is a Hamiltonian path between every pair of vertices.