关于图测地数的几个问题(英文)  

SOME RESULTS ON GEODETIC NUMBER OF GRAPHS

作　　者：刘庆敏[1] 吕长虹[1] 董林[1] 

机构地区：[1]华东师范大学数学系,上海200062

出　　处：《数学杂志》2008年第1期8-14,共7页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(No.10301010);Science and Technology Commission of Shanghai Municipality(No.04JC14031).

摘　　要：本文研究了图的测地数.利用极点必属于测地集的方法,刻画了g(G)=n-1的图G的结构,同时使用图的一些重要参数,获得了图上下测地数的几个新的界.对于有向图D,讨论了g(D)=2的充要条件.In this paper, we mainly sutdy the geodetic number of a graph G. Based on the lemma which the extreme vertex belong to any geodetic set of graph, we get the upper and lower geodetic numbers of the graphs G with g（G）=n-1. Secondly, some new bounds for upper and lower geodetic numbers of G are raised from some important parameters of the graph. Finally, for a digraph D, a sufficient and necessary condition for g（D）= 2 is given.

关 键 词：有向图 测地集 测地数 

分 类 号：O153.3[理学—数学]