标题： 谱充分条件用于图因子 显示英文标题

标题： Spectral Sufficient Conditions for Graph Factors

摘要： 图的$\{K_{1,1}, K_{1,2},C_m: m\geq3\}$因子是一个生成子图，其每个连通分支都是$\{K_{1,1}, K_{1,2},C_m: m\geq3\}$的元素。 在本文中，通过图谱方法，我们建立了无符号拉普拉斯谱半径的下界和距离谱半径的上界，以确定图是否具有$\{K_2\}$因子。 我们得到了$G$的大小（或谱半径）的下界，以保证$G$包含$\{K_{1,1}, K_{1,2},C_m: m\geq3\}$因子。 然后我们确定$G$的距离谱半径的上界，以确保$G$具有$\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-因子。 此外，通过构造极图，我们证明了上述所有界都是最佳的。 显示英文摘要

摘要： The $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor of a graph is a spanning subgraph whose each component is an element of $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$. In this paper, through the graph spectral methods, we establish the lower bound of the signless Laplacian spectral radius and the upper bound of the distance spectral radius to determine whether a graph admits a $\{K_2\}$-factor. We get a lower bound on the size (resp. the spectral radius) of $G$ to guarantee that $G$ contains a $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor. Then we determine an upper bound on the distance spectral radius of $G$ to ensure that $G$ has a $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor. Furthermore, by constructing extremal graphs, we show that the above all bounds are best possible.