On the fault diameter and wide diameter of the exchanged 3-ary $n$-cube

Fault diameter and wide diameter are two critical parameters for evaluating communication performance in interconnection networks. They measure the fault tolerance and transmission efficiency of networks. The exchanged 3-ary $n$-cube is a recently proposed variant of the hypercube, denoted by $E3C(r,s,t)$. In this work, we obtain that the $(2r+1)$-fault diameter and $(2r+2)$-wide diameter of $E3C(r,s,t)$ are bounded between $n+3$ and $n+5$ for $1\le r\le s\le t$.