论文标题
频谱甚至循环问题
The spectral even cycle problem
论文作者
论文摘要
在本文中，我们研究了不包含给定长度的均匀周期的大级图的最大邻接光谱半径。对于$ n> k $，令$ s_ {n，k} $为$ k $ vertices上的一个集团的联接，带有独立的$ n-k $ vertices，并用$ s_ {n，k}^+$表示从$ s_ {n，k}获得的图表，通过添加一个边缘。在2010年，Nikiforov指出，对于足够大的$ n $，$ c_ {2k+2} $ - 最大光谱半径的免费图为$ s_ {n，k}^+$，并且$ \ {c_ {2k+1}，c_ {2k+2} $ s $ s $ s_ $ s_ $ s_我们解决了这两个部分的猜想。
In this paper, we study the maximum adjacency spectral radii of graphs of large order that do not contain an even cycle of given length. For $n>k$, let $S_{n,k}$ be the join of a clique on $k$ vertices with an independent set of $n-k$ vertices and denote by $S_{n,k}^+$ the graph obtained from $S_{n,k}$ by adding one edge. In 2010, Nikiforov conjectured that for $n$ large enough, the $C_{2k+2}$-free graph of maximum spectral radius is $S_{n,k}^+$ and that the $\{C_{2k+1},C_{2k+2}\}$-free graph of maximum spectral radius is $S_{n,k}$. We solve this two-part conjecture.
