On the Lict Geodetic Number of a Graph

For any graph G=(V,E) , the lict graph of G denoted by ( ) G η . The Lict graph ( ) G η of a graph G as the graph whose vertex set is the union of the set of edges and the set of cut vertices of G in which two vertices are adjacent if and only if the corresponding edg es of G are adjacent or the corresponding members are incident. For two vertices u and v of G, the s et I(u,v) consists of all vertices lying on a u-v geodesic in G. If S is a set of vertices of G, then I(S) i s the union of all sets I(u,v) for vertices u and v in S. The geodetic number g(G) is the minimum cardinality mong the subsets S of V(G) with I(S)=V(G). In this paper we obtain the geodetic number of lict graph of any graph. Also, obtain many bounds on geodetic number in terms of elements of G.