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2011 | 31 | 3 | 493-507
Tytuł artykułu

The hull number of strong product graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Kategorie tematyczne
Wydawca
Rocznik
Tom
31
Numer
3
Strony
493-507
Opis fizyczny
Daty
wydano
2011
otrzymano
2009-09-23
poprawiono
2010-07-23
zaakceptowano
2010-07-23
Twórcy
  • Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai-627 002, India
  • Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai-627 002, India
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1560
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