摘要
对于图G(或有向图D)内的任意两点u和v,u—v测地线是指在u和v之间(或从u到v)的最短路.I(u,v)表示位于u—v测地线上所有点的集合,对于S(?)V(G)(或V(D)),I(S)表示所有I(u,v)的并,这里u,v∈S.G(或D)的测地数g(G)(或g(D))是使I(S)=V(G)(或I(S)=V(D))的点集S的最小基数.G的下测地数g^-(G)=min{g(D):D是G的定向图},G的上测地数g^+(G)=max{g(D):D是G的定向图}.对于u∈V(G)和v∈V(H),G_u+H_v表示在u和v之间加一条边所得的图.本文主要研究图G_u+H_v的测地数和上(下)测地数.
For any two vertices u and v in a graph G (digraph D, respectively), a u - v geodesic is a shortest path between u and v (from u to v, respectively). 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) (g(D), respectively) of a graph G (digraph D, respectively) is the minimum cardinality of a set S with Ⅰ(S) = V(G) (Ⅰ(S) = V(D), respectively). The lower geodetic number of G is 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}. For two graphs G and H with u C V(G) and v C V(H), Gu + Hv is a graph obtained from G and H by adding an edge uv. The main purpose of this paper is to study the lower and upper geodetic numbers of the graph Gu +Hv.
出处
《运筹学学报》
CSCD
北大核心
2006年第3期33-40,共8页
Operations Research Transactions
基金
Supported in part by National Natural Science Foundation of China(No.10301010)
and Science and Technology Commission of Shanghai Municipality(No.04JC14031).
关键词
运筹学
凸集
完全r-部图
测地线
测地数
Operation research, convex set, complete r-partite graph, geodesic, geodetic number