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2008

On the geodetic number and related metric sets in Cartesian product graphs

10 years 1 months ago
On the geodetic number and related metric sets in Cartesian product graphs
A set S of vertices of a graph G is a geodetic set if every vertex of G lies in at least one interval between the vertices of S. The size of a minimum geodetic set in G is the geodetic number of G. Upper bounds for the geodetic number of Cartesian product graphs are proved and for several classes exact values are obtained. It is proved that many metrically defined sets in Cartesian products have product structure and that the contour set of a Cartesian product is geodetic if and only if their projections are geodetic sets in factors. 2000 Mathematical Subject Classification: 05C12
Bostjan Bresar, Sandi Klavzar, Aleksandra Tepeh Ho
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where DM
Authors Bostjan Bresar, Sandi Klavzar, Aleksandra Tepeh Horvat
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