Abstract:

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 2 E by a suspended arc (path) Pg(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.

Key words: Geodetic block, subdivision.