# The hull number of strong product graphs

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

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 3, page 493-507
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topA.P. Santhakumaran, and S.V. Ullas Chandran. "The hull number of strong product graphs." Discussiones Mathematicae Graph Theory 31.3 (2011): 493-507. <http://eudml.org/doc/270792>.

@article{A2011,

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.},

author = {A.P. Santhakumaran, S.V. Ullas Chandran},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {strong product; geodetic number; hull number; extreme hull graph},

language = {eng},

number = {3},

pages = {493-507},

title = {The hull number of strong product graphs},

url = {http://eudml.org/doc/270792},

volume = {31},

year = {2011},

}

TY - JOUR

AU - A.P. Santhakumaran

AU - S.V. Ullas Chandran

TI - The hull number of strong product graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 3

SP - 493

EP - 507

AB - 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.

LA - eng

KW - strong product; geodetic number; hull number; extreme hull graph

UR - http://eudml.org/doc/270792

ER -

## References

top- [1] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley, Redwood City, CA, 1990). Zbl0688.05017
- [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. Zbl1081.05100
- [3] G. Chartrand, F. Harary and P. Zhang, On the hull number of a graph, Ars Combin. 57 (2000) 129-138. Zbl1064.05049
- [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. Zbl1009.05051
- [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. Zbl0987.05047
- [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. Zbl1027.05034
- [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. Zbl0584.05044
- [9] W. Imrich and S. Klavžar, Product graphs: Structure and Recognition (Wiley-Interscience, New York, 2000). Zbl0963.05002
- [10] T. Jiang, I. Pelayo and D. Pritikin, Geodesic convexity and Cartesian product in graphs, manuscript.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.