扇图的笛卡儿积的测地数(英文)

对于图G内的任意两点u和v,u-v测地线是指u和v之间的最短路.I(u,v)表示位于u-v测地线上所有点的集合,对于V(G)S,I(S)表示所有I(u,v)的并,这里u,v∈S.G的测地数g(G)是使I(S)=V(G)的点集S的最小基数.文章研究了Pm×Fn和Cm×Fn的测地数,这里Pm表示m阶路,Cm表示m阶圈,Fn表示n阶扇图。

Geodetic Numbers of Cartesian Products of Fan Graphs

For any two vertices u and v in a graph G, a u - v geodesic is a shortest path between u and v. Let I( u, v) denote the set of all the vertices lying on a u - v geodesic. For a vertex subset S(U)V( G), let I(S) = U u,v∈S I( u, v). The geode-tic number g(G) of a graph G is the minimum cardinality of a set S with I(S) = V(G). The main purpose of this paper is to study the geodetic numbers of Pm× Fn and Cm× Fn, where Pm is a path of order m, Cm is a cycle of order m and Fn is a fan graph of order n.