报告题目 (Title)：平面图的最大spread (On the maximum spread of planar graphs)
报告人 (Speaker)： 王智宇 博士（佐治亚理工学院）
报告时间 (Time)：2023年7月7日(周五) 9:00
报告地点 (Place)：校本部F309
邀请人(Inviter)：康丽英
报告摘要：The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$. Gotshall, O'Brien and Tait conjectured that for sufficiently large $n$, the $n$-vertex outerplanar graph with maximum spread is the graph obtained by joining a vertex to a path on $n-1$ vertices. In this paper, we disprove this conjecture by showing that the extremal graph is the graph obtained by joining a vertex to a path on $\lceil(2n-1)/3\rceil$ vertices and $\lfloor(n-2)/3\rfloor$ isolated vertices. For planar graphs, we show that the extremal $n$-vertex planar graph attaining the maximum spread is the graph obtained by joining two nonadjacent vertices to a path on $\lceil(2n-2)/3\rceil$ vertices and $\lfloor(n-4)/3\rfloor$ isolated vertices.