摘要
对于图G(或者有向图D)内的任意两点u和v,u-v测地线是指在u和v之间的最短路(或者从u到v).I(u,v)表示位于一条u-v测地线上所有点的集合,对于SV(G),I(S)表示所有I(u,v)的并,这里u,v∈S.图G(或者有向图D)的测地数g(G)(g(D))是使I(S)=V(G)(I(S)=V(D))的最小点集S的基数.定义G的所有定向图中测地数的最小值为G的下测地数,即g-(G)=min{g(D):D是G的定向图};定义G的所有定向图中测地数的最大值为G的上测地数,即g+(G)=max{g(D):D是G的定向图}.本文的主要目的是研究G∨H的上、下测地数,此外,文章给出了g(G)=g(G×P3)的一个充分必要条件.
For any two vertices u and υin a graph G(or digraph D),a u-υ geodesic is a shortest path between u andυ(or from u to υ).Let I(u,υ)denote the set of all vertices lying on a u-υ geodesic.For a vertex subset S,let I(S)denote the union of all I(u,υ)for u,υ∈ S.The geodetic number g(G) (or g(D))of a graphG(or digraph D)is the minimum cardinality of a set S with I(S)=V(G)(or I(S)=V(D)).The lower geodetic number of Gis g-(G)=min{g(D):D is an orientation of G}.The upper geodetic number of G is g+(G)=max{g(D):D is an orientation of G}.The main purpose of this papers to study the upper and lower geodetic number of G V H.In addition,a sufficient and necessary condition for g(G)=g(G×P3)is presented.
出处
《应用数学》
CSCD
北大核心
2007年第4期717-725,共9页
Mathematica Applicata
基金
Supported by National Natural Science Foundation of China (10301010)
Science and Technology Commission of Shanghai Municipality (04JC14031)
National Natural Science Founda-tion of Anhui (2006KJ256B)
关键词
凸集
笛卡尔积
测地线
测地数
Convex set
Cartesian product
Geodesic
Geodetie number