关于圈与完全图的笛卡儿积的测地数

The Geodetic Number of Cartesian Product on Cycles and Complete Graphs

对于图G内的任意两点u和v,在u和v之间的最短路称为u-v测地线.I(u,v)表示位于u-v测地线上所有点的集合,对于S V(G),I(S)表示所有I(u,v)的并,这里u,v∈S.如果I(S)=V(G),那么称S是G的测地集;并把测地集的最小基数称为G的测地数,记为g(G).文章主要研究Cn×K3的测地数.

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 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. If I（S） = V（G）,then S is a geodetic set of G. The minimum cardinality of a geodetic set in G is named the geodetic number of G, denoted g（G）. In this paper, we explore the geodetic number on Cn×K3.