论文标题
带有完整的两分图作为星形补充的常规图
Regular graphs with a complete bipartite graph as a star complement
论文作者
论文摘要
令$ g $是订单$ n $的图表，$μ$是$ g $的邻接特征值$ k \ geq 1 $。 $ g $中的$μ$ $ h $的一颗星级是$ g $ $ g $ n-k $的子图，没有特征$ $μ$，而顶点子集$ x = v（g-h）$称为$ g $中的$μ$。星形补充和恒星集的研究提供了图结构与线性代数之间的牢固联系。在本文中，我们以$ k_ {t，s} \（s \ geq t \ geq 2）$研究了常规图，作为特征值$μ$的明星补充，尤其是，尤其是，$ t = 3 $的情况完全特征，在$ t = s = S $时获得一些属性，并提出一些问题以进一步研究。
Let $G$ be a graph of order $n$ and $μ$ be an adjacency eigenvalue of $G$ with multiplicity $k\geq 1$. A star complement $H$ for $μ$ in $G$ is an induced subgraph of $G$ of order $n-k$ with no eigenvalue $μ$, and the vertex subset $X=V(G-H)$ is called a star set for $μ$ in $G$. The study of star complements and star sets provides a strong link between graph structure and linear algebra. In this paper, we study the regular graphs with $K_{t,s}\ (s\geq t\geq 2)$ as a star complement for an eigenvalue $μ$, especially, characterize the case of $t=3$ completely, obtain some properties when $t=s$, and propose some problems for further study.
