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arXiv · 2603.16396

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

Stuart E. Anderson
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Abstract

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 $\lfloor n/2\rfloor+2$. We prove that $G_3$ and $G_4$ are Ramanujan graphs, satisfying $|λ_2| \le 2\sqrt{5}$. 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.

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Stuart E. Anderson. 2026-03-17. An Infinite Family of 6_Regular B-Cayley Graphs from the Petersen Graph. https://arxiv.org/abs/2603.16396

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