Geodetic Numbers of Cartesian Products of Fan Graphs
XU Shao-yuan · 2010
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 V(G)S,let I(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.