应用数学2007，Vol.20Issue(1)：158-163,6.
图的笛卡儿积的测地数
The Geodetic Numbers of Cartesian Products of Graphs
摘要
Abstract
For any two vertices u and v in a graph G,a u-v geodesic is the shortest path between u and v.Let I(u,v) denote the set of all vertices lying on a u-v geodesic.For a vertex subset S,let I(S) denote the union of all I(u,v) for u,v∈S.The geodetic number g(G) of a graph G is the minimum cardinality of a set S with I(S)=V(G).In this paper,a sufficient and necessary condition for the equality of g(G) and g(G×K3) is presented,and for a tree T,we give the geodetic number of T×Km and Cn×Km.关键词
凸集/笛卡儿积/测地线/测地数Key words
Convex set/Cartesian product/Geodesic/Geodetic number分类
数理科学引用本文复制引用
叶永升,吕长虹,刘庆敏..图的笛卡儿积的测地数[J].应用数学,2007,20(1):158-163,6.基金项目
Supported by the National Natural Science Foundation of China (10301010),Science and Technology Commission of Shanghai Municipality (04JC14031),and National Natural Science Foundation of Anhui (2006KJ256B) （10301010）
