ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 31(3) (2011) 493-507
DOI: 10.7151/dmgt.1560

The hull number of strong product graphs

A.P. Santhakumaran and S.V. Ullas Chandran

Department of Mathematics
St. Xavier's College (Autonomous)
Palayamkottai-627 002, India


For a connected graph G with at least two vertices and S a subset of vertices, the convex hull [S]G is the smallest convex set containing S. The hull number h(G) is the minimum cardinality among the subsets S of V(G) with [S]G = V(G). Upper bound for the hull number of strong product G☒ H of two graphs G and H is obtainted. Improved upper bounds are obtained for some class of strong product graphs. Exact values for the hull number of some special classes of strong product graphs are obtained. Graphs G and H for which h(G☒ H) = h(G)h(H) are characterized.

Keywords: strong product, geodetic number, hull number, extreme hull graph

2010 Mathematics Subject Classification: 05C12.


[1]F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley, Redwood City, CA, 1990).
[2]G. B. Cagaanan and S.R. Canoy, Jr., On the hull sets and hull number of the Composition graphs, Ars Combin. 75 (2005) 113--119.
[3]G. Chartrand, F. Harary and P. Zhang, On the hull number of a graph, Ars Combin. 57 (2000) 129--138.
[4]G. Chartrand and P. Zhang, Extreme geodesic graphs, Czechoslovak Math. J. 52 (127) (2002) 771--780, doi: 10.1023/B:CMAJ.0000027232.97642.45.
[5]G. Chartrand, F. Harary and P. Zhang, On the Geodetic Number of a Graph, Networks 39 (2002) 1--6, doi: 10.1002/net.10007.
[6]G. Chartrand, J.F. Fink and P. Zhang, On the hull Number of an oriented graph, Int. J. Math. Math Sci. 36 (2003) 2265--2275, doi: 10.1155/S0161171203210577.
[7]G. Chartrand and P. Zhang, Introduction to Graph Theory (Tata McGraw-Hill Edition, New Delhi, 2006).
[8]M.G. Everett and S.B. Seidman, The hull number of a graph, Discrete Math. 57 (1985) 217--223, doi: 10.1016/0012-365X(85)90174-8.
[9]W. Imrich and S. Klavžar, Product graphs: Structure and Recognition (Wiley-Interscience, New York, 2000).

Received 23 September 2009
Revised 23 July 2010
Accepted 23 July 2010