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

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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

Abstract

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.

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