id: 05885812
dt: j
an: 05885812
au: Santhakumaran, A.P.; Ullas Chandran, S.V.
ti: The geodetic number of strong product graphs.
so: Discuss. Math., Graph Theory 30, No. 4, 687-700 (2010).
py: 2010
pu: University of Zielona Góra Press, Zielona Góra
la: EN
cc: 
ut: geodetic number; extreme vertex; extreme geodesic graph; open geodetic
    number; double domination number
ci: 
li: doi:10.7151/dmgt.1523
ab: Summary: 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 $u,v \in S$ is denoted by $I_G[S]$. A set $S\subseteq
    V(G)$ 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.
rv: