论文标题
不规则两分图的最大光谱半径
The maximum spectral radius of irregular bipartite graphs
论文作者
论文摘要
如果两部分图是亚基，如果它是最大程度三分的不规则二分图。在本文中，我们证明，在$ n $的亚地下双分部分图上，最大光谱半径的渐近值为$ 3- \ vartheta（\ frac {π^{2}}} {n^{2}}}）$。我们的关键方法是由于Willms而充分利用某些Tridiagonal矩阵的特征值[Siam J. Matrix肛门。应用。 30（2008）639--656]。此外，对于很大的最高度，即，最大程度至少为$ \ lfloor n/2 \ rfloor $，我们表征具有最大光谱半径的不规则二分图。对于一般的最大程度，我们在不规则二分图的光谱上呈现上限，就顺序和最大程度而言。
A bipartite graph is subcubic if it is an irregular bipartite graph with maximum degree three. In this paper, we prove that the asymptotic value of maximum spectral radius over subcubic bipartite graphs of order $n$ is $3-\varTheta(\frac{π^{2}}{n^{2}})$. Our key approach is taking full advantage of the eigenvalues of certain tridiagonal matrices, due to Willms [SIAM J. Matrix Anal. Appl. 30 (2008) 639--656]. Moreover, for large maximum degree, i.e., the maximum degree is at least $\lfloor n/2 \rfloor$, we characterize irregular bipartite graphs with maximum spectral radius. For general maximum degree, we present an upper bound on the spectral radius of irregular bipartite graphs in terms of the order and maximum degree.
