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arXiv · 1705.04610

Vector spaces and Grassmann graphs over residue class rings

Li-Ping Huang·Benjian Lv·Kaishun Wang
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Abstract

Let $\mathbb{Z}_{p^s}$ be the residue class ring of integers modulo $p^s$, where $p$ is a prime number and $s$ is a positive integer. Using matrix representation and the inner rank of a matrix, we study the intersection, join, dimension formula and dual subspaces on vector subspaces of $\mathbb{Z}^n_{p^s}$. Based on these results, we investigate the Grassmann graph $G_{p^s}(n,m)$ over $\mathbb{Z}_{p^s}$. $G_{p^s}(n,m)$ is a connected vertex-transitive graph, and we determine its valency, clique number and maximum cliques. Finally, we characterize the automorphisms of $G_{p^s}(n,m)$.

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Li-Ping Huang, Benjian Lv, Kaishun Wang. 2017-05-12. Vector spaces and Grassmann graphs over residue class rings. https://arxiv.org/abs/1705.04610

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