## Untitled

##### Abstract

o et al. introduced the alternating group graph as an interconnection network topology for computing systems. The concept of panconnected graphs was proposed by Alavi and Williamson. A graph $G$ with vertex set $V(G)$ is panconnected if for every any two vertices $x$ and $y$, there exists a path of length $l$ joining $x$ and $y$ for every $l$ such that $d_G(x,y) \leq l \leq |V(G)|-1$, where $d_G(x,y)$ represents the distance between $x$ and $y$ in the graph $G$, the length of the shortest path joining $x$ and $y$. J-M Chang et al. showed that the alternating group graph $AG_n$ is panconnected. In this paper we consider a class of Cayley graphs introduced by Cheng et al. that are generated by certain 3-cycles on the alternating group $A_n$. These graphs are generalizations of the alternating group graph $AG_n$. We look at the case when the 3-cycles from a ~``tree-like structure", and analyze the panconnectivity of these graphs. We prove that this family of Cayley graphs is panconnected.