论文标题
图形的稀疏性允许两个不同的特征值
Sparsity of Graphs that Allow Two Distinct Eigenvalues
论文作者
论文摘要
图$ g $的参数$ q（g）$是$ g $所描述的对称矩阵家族中不同特征值的最小数量。结果表明，如果$ n $偶数，则连接的图形$ g $所需的最小边数为$ q（g）= 2 $是$ 2N-4 $，如果$ n $是奇数，则$ 2N-3 $。另外，给出了在任何一种情况下都实现平等的图表的表征。
The parameter $q(G)$ of a graph $G$ is the minimum number of distinct eigenvalues over the family of symmetric matrices described by $G$. It is shown that the minimum number of edges necessary for a connected graph $G$ to have $q(G)=2$ is $2n-4$ if $n$ is even, and $2n-3$ if $n$ is odd. In addition, a characterization of graphs for which equality is achieved in either case is given.
