黄怡,陈美润

• 1:新疆石油学院
• 2:厦门大学数学科学学院

摘要(Abstract)：

强有向图D中任意两个点u,v的强距离sd(u,v)定义为D中包含u和v的最小有向强子图Duv的大小(弧的数目).D中一点u的强离心率se(u)定义为u到其他顶点的强距离的最大值.强有向图D的强半径srad(D)(相应的强直径sdiam(D))定义为D中所有顶点强离心率的最小值(相应的最大值).无向图G的最小定向强半径srad(G)(相应的最大定向强半径SRAD(G))定义为D中所有强定向的强半径的最小值(相应的最大值).无向图G的最小定向强直径sdiam(G)(相应的最大定向强直径SDIAM(G))定义为D中所有强定向的强直径的最小值(相应的最大值).本文确定了路和路的笛卡尔积的最小定向强半径srad(Pm×Pn)和强直径的值sdiam(Pm×Pn),给出了最大定向强半径SRAD(Pm×Pn)的界并提出关于最大定向强直径SDIAM(Pm×Pn)的一个猜想.

关键词(KeyWords)： 强距离;最小定向强半径和强直径;最大定向强半径和强直径

Abstract:

Keywords:

基金项目(Foundation):

作者(Author): 黄怡,陈美润

参考文献(References)：

• [1]Bang-Jensen J,Gutin G.Digraphs:Theory,Algorithms and Applications[M].Springer,London,2000.
• [2]Chartrand G,Erwin D,Raines M,Zhang P.Strong Distance in Strong Digraphs[J].J Combin Math Combin Comput, 1999,31:33-44.
• [3]Chartrand G,Erwin D,Raines M,Zhang P.On Strong Distance in Strong Oriented Graphs[J].Congr Numer,1999,138: 49-63.
• [4]Chen Meirun,Guo Xiaofeng,Li Hao.Bounds on Strong Diameter in Oriented Graphs.Applied Mathematics Letters,in press.
• [5]Chen Meirun,Guo Xiaofeng.Lower and Upper Orientable Strong Radius and Strong Diameter of Cartesian Product of Complete Graphs.Ars Combinatoria,in press.
• [6]Peter Dankelmann,Henda C.Swart,David P.Day.On Strong Distance in Oriented Graphs[J].Discrete Math,2003,266: 195-201.
• [7]Lai Yungling,Chiang Fenghsu,Lin Chuhe,Yu Tungchin.Strong Distance of Complete Bipartite Graphs,The 19th Workshop on Combinatorial Mathematics and Computation Theory[M].2002,12-16.
• [8]Miao Huifang,Guo Xiaofeng.Lower and Upper Orientable Strong Radius and Strong Diameter of Complete k-Partite Graphs[J].Discrete Applied Mathematics,2006,154(11):1606-1614.
• [9]Miao Huifang,Guo Xiaofeng.Strong Distance in Strong Oriented Complete k-Partite Graphs.Ars Combinatoria,in press.