论文标题
从边缘集团分区确定的图的最小特征值上的急剧界限
Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
论文作者
论文摘要
提出了任意图的最小特征值的尖锐边界。使用边缘集团分区推导下下部（上）的必要和足够（仅足够）条件。作为一个应用程序，我们证明，对于每个$ n \ ge 4 $，$ n $ Queens'Graph $ \ Mathcal {Q}（n）$的最低特征值等于$ -4 $，并且也证明了此eigenValue的多重性IS $（n-3）^2 $。此外，还获得了边缘分区图参数上的一些结果。
Sharp bounds on the least eigenvalue of an arbitrary graph are presented. Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduced using edge clique partitions. As an application, we prove that the least eigenvalue of the $n$-Queens' graph $\mathcal{Q}(n)$ is equal to $-4$ for every $n \ge 4$ and it is also proven that the multiplicity of this eigenvalue is $(n-3)^2$. Additionally, some results on the edge clique partition graph parameters are obtained.
