Geodesic
The geodetic number of strong product graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 687-700

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For two vertices u and v of a connected graph G, the set I_G[u,v] consists of all those vertices lying on u-v geodesics in G. Given a set S of vertices of G, the union of all sets I_G[u,v] for u,v ∈ S is denoted by I_G[S]. A set S ⊆ V(G) is a geodetic set if I_G[S] = V(G) and the minimum cardinality of a geodetic set is its geodetic number g(G) of G. Bounds for the geodetic number of strong product graphs are obtainted and for several classes improved bounds and exact values are obtained.
Keywords: geodetic number, extreme vertex, extreme geodesic graph, open geodetic number, double domination number 
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Santhakumaran, A.; Ullas Chandran, S. The geodetic number of strong product graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 687-700. http://geodesic.mathdoc.fr/item/DMGT_2010_30_4_a12/