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.
出处
《数学杂志》
CSCD
北大核心
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).
关键词
有向图
测地集
测地数
digraph geodetic set geodetic number
