论文标题
立方顶点传递图的简单特征值
Simple eigenvalues of cubic vertex-transitive graphs
论文作者
论文摘要
如果$ v $是图$ x $的特征值$λ$，而$α$是$ x $的$λ$，那么$α（v）$也是$λ$的特征。因此，简单的顶点传播图的特征值是相当不错的。我们研究了具有非平凡的简单特征值的立方顶点传递图，并发现与弧线传递，常规地图和Chebyshev多项式的显着连接。
If $v$ is an eigenvector for eigenvalue $λ$ of a graph $X$ and $α$ is an automorphism of $X$, then $α(v)$ is also an eigenvector for $λ$. Thus it is rather exceptional for an eigenvalue of a vertex-transitive graph to be simple. We study cubic vertex-transitive graphs with a non-trivial simple eigenvalue, and discover remarkable connections to arc-transitivity, regular maps and Chebyshev polynomials.
