EDGE SUBDIVISIONS OF A GIVEN GEODETIC BLOCK PRESERVING ITS PROPERTY TO BE GEODETIC

In this paper authors have obtained a new necessary and sufficient condition for a graph G to be a geodetic graph. Let g : E → Z₊ be a function from the set of edges of a graph G to the set of nonnegative integers and let g(G) denote the graph obtained from G by replacing each edge e ∈ E by a suspended arc (path) P_g(e)+2 of length g(e) + 1. and by using this condition, established a criterion for a function g to be a function which can generate a new geodetic block g(G) from a given geodetic block G.