Geodesic
The hull number of strong product graphs
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 493-507.

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMGT_2011_31_3_a5,
     author = {Santhakumaran, A. and Ullas Chandran, S.},
     title = {The hull number of strong product graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {493--507},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2011_31_3_a5/}
}
TY  - JOUR
AU  - Santhakumaran, A.
AU  - Ullas Chandran, S.
TI  - The hull number of strong product graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2011
SP  - 493
EP  - 507
VL  - 31
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2011_31_3_a5/
LA  - en
ID  - DMGT_2011_31_3_a5
ER  - 
%0 Journal Article
%A Santhakumaran, A.
%A Ullas Chandran, S.
%T The hull number of strong product graphs
%J Discussiones Mathematicae. Graph Theory
%D 2011
%P 493-507
%V 31
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2011_31_3_a5/
%G en
%F DMGT_2011_31_3_a5
Santhakumaran, A.; Ullas Chandran, S. The hull number of strong product graphs. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 493-507. http://geodesic.mathdoc.fr/item/DMGT_2011_31_3_a5/

[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).

[10] T. Jiang, I. Pelayo and D. Pritikin, Geodesic convexity and Cartesian product in graphs, manuscript.