Linearly many faults in 2‐tree‐generated networks

In this article we consider a class of Cayley graphs that are generated by certain 3‐cycles on the alternating group An. These graphs are generalizations of the alternating group graph AGn. We look at the case when the 3‐cycles form a “tree‐like structure,” and analyze its fault resiliency. We present a number of structural theorems and prove that even with linearly many vertices deleted, the remaining graph has a large connected component containing almost all vertices.