The geodetic number of a graph (original) (raw)

We introduce a new graph theoretic parameter, the geodetic number of a connected graph G = (V, E) as follows. The geodetic closure of a node set S C V is the set of all nodes '11 E V which lie in some geodesic in G joining two nodes I and y of 5'. The geodetic number of a connected graph G, denoted by g(G), is the minimum number of nodes in a set S' whose geodetic closure is all of V. We show that the determination of g(G) is an NP-hard problem and its decision problem is NP-complete, and present an algorithm for finding g(G).