SOME RESULTS ON GEODETIC NUMBER OF GRAPHS
Liu Qing-min · Journal of Mathematics · 2008
In this paper, we mainly sutdy the geodetic number of a graph G. Based on the lemma which the extreme vertex belong to any geodetic set of graph, we get the upper and lower geodetic numbers of the graphs G with g(G)=n-1. Secondly, some new bounds for upper and lower geodetic numbers of G are raised from some important parameters of the graph. Finally, for a digraph D, a sufficient and necessary condition for g(D)=2 is given.