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arXiv 2510.02400math.CO
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强正则图双倍覆盖的距离谱

The distance spectrum of the bipartite double cover of strongly regular graphs

Lorestan University（洛雷斯坦大学）

S. Morteza Mirafzal

备注：
13 pages, 1 figure
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AI总结：

研究强正则图双倍覆盖的距离谱，揭示其与原图谱的关系，明确确定双倍覆盖图的距离谱。

摘要：

一个参数为(n,d,a,c)的强正则图是一个d-正则图，其中每对相邻顶点有恰好a个公共邻居，每对非相邻顶点有恰好c个公共邻居。设G=(V,E)的顶点数为n，G的距离矩阵D=D(G)是一个n×n矩阵，其行和列按V索引，使得D_{uv}=d_G(u,v)=d(u,v)，其中d_G(u,v)是图G中顶点u和v之间的距离。本文旨在确定强正则图族的双倍覆盖的距离谱。换句话说，设G=(V,E)是一个参数为(n,k,a,c)的强正则图。我们展示G的谱与其双倍覆盖B(G)的距离谱之间存在紧密关系。我们根据G的谱显式确定B(G)的距离谱。事实上，根据G的参数。

英文摘要：

A strongly regular graph with parameters $(n,d,a,c)$ is a $d$-regular graph of order $n$, in which every pair of adjacent vertices has exactly $a$ common neighbor(s) and every pair of nonadjacent vertices has exactly $c$ common neighbor(s). Let $n$ be the number of vertices of the graph $G=(V,E)$. The distance matrix $D=D(G)$ of $G$ is an $n \times n $ matrix with the rows and columns indexed by $V$ such that $D_{uv} = d_{G}(u, v)=d(u,v)$, where $d_{G}(u, v)$ is the distance between the vertices $u$ and $v$ in the graph $G$. In this paper, we are interested in determining the distance spectrum of the bipartite double cover of the family of strongly regular graphs. In other words, let $G=(V,E)$ be a strongly regular graph with parameters $(n,k,a,c)$. We show that there is a close relationship between the spectrum of $G$ and the distance spectrum of $B(G)$, where $B(G)$ is the double cover of $G$. We explicitly determine the distance spectrum of the graph $B(G)$, according to the spectrum of $G$. In fact, according to the parameters of the graph $G$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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