论文标题
$ k_ {2，t} $的最大传播 - 无少量图
Maximum spread of $K_{2,t}$-minor-free graphs
论文作者
论文摘要
图$ g $的传播是$ g $的邻接矩阵的最大和最小特征值之间的差异。在本文中，我们考虑包含不包含$ k_ {2，t} $的图形家庭。我们表明，对于任何$ t \ geq 2 $，都有一个整数$ξ_t$，使得$ n $ vertex $ k_ {2，t} $的最大传播是通过将顶点与$ \ lfloor \ frac \ frac $ \ frac {2n+ploor的差异结合而获得的图表来实现的。 $ k_t $和$ n -1 -t \ lfloor \ frac {2n+ξ_t} {3T} \ rfloor $隔离顶点。极端图是唯一的，除非$ t \ equiv 4 \ mod 12 $和$ \ frac {2n+ξ_t} {3t} $是一个整数，在这种情况下，另一个极端图是通过将顶点连接到$ \ lfloor \ frac \ frac {2n+ eceror的distertex获得的图表， $ k_t $和$ n-1-t（\ lfloor \ frac {2n+ξ_t} {3T} \ rfloor-1）$隔离顶点。此外，我们给出了$ξ_t$的明确公式。
The spread of a graph $G$ is the difference between the largest and smallest eigenvalues of the adjacency matrix of $G$. In this paper, we consider the family of graphs which contain no $K_{2,t}$-minor. We show that for any $t\geq 2$, there is an integer $ξ_t$ such that the maximum spread of an $n$-vertex $K_{2,t}$-minor-free graph is achieved by the graph obtained by joining a vertex to the disjoint union of $\lfloor \frac{2n+ξ_t}{3t}\rfloor$ copies of $K_t$ and $n-1 - t\lfloor \frac{2n+ξ_t}{3t}\rfloor$ isolated vertices. The extremal graph is unique, except when $t\equiv 4 \mod 12$ and $\frac{2n+ ξ_t} {3t}$ is an integer, in which case the other extremal graph is the graph obtained by joining a vertex to the disjoint union of $\lfloor \frac{2n+ξ_t}{3t}\rfloor-1$ copies of $K_t$ and $n-1-t(\lfloor \frac{2n+ξ_t}{3t}\rfloor-1)$ isolated vertices. Furthermore, we give an explicit formula for $ξ_t$.
