An Infinite Family of 6_Regular B-Cayley Graphs from the Petersen Graph

We construct an infinite family of 6-regular graphs $\{G_n{\}}_{n\ge 3}$ by taking $n$ copies of the Petersen graph and wiring corresponding vertices according to an $n$-cycle permutation. Each $G_n$ has $10n$ vertices, $30n$ edges, and automorphism group $D_{5n}$ of order $10n$, acting with two vertex orbits of size $5n$. The graphs have girth $4$ and diameter $\lfloor n\mathrm{/}2\rfloor +2$. We prove that $G_3$ and $G_4$ are Ramanujan graphs, satisfying $\mathrm{\mid }{\lambda }_2\mathrm{\mid }\le 2\sqrt{5}$. The first five members ($n=3,\dots ,7$) have been deposited in the House of Graphs database as entries 56324–56328. This construction provides new examples of highly symmetric regular graphs and contributes two new Ramanujan graphs to the literature. All computational scripts are available online for full reproducibility.