Diameter formulas for a class of undirected multi-loop networks

Let $n\ge 5$ and $m\ge 1$ be positive integers. Let $S=(s_1,s_2,\dots ,s_m)$ be a sequence of integers such that $1\le s_1<s_2<\dots <s_m\le \lfloor \frac{n-1}{2}\rfloor \mathrm{.}$ In this paper, we discuss the diameter of multi-loop networks $C_n(s_1,s_2,\dots ,s_m)$ when $s_1=1$. We also present a relation between the diameter of multi-loop networks and the diameter of generalized Petersen graphs.