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2011 | 31 | 1 | 171-181
Tytuł artykułu

The forcing steiner number of a graph

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a connected graph G = (V,E), a set W ⊆ V is called a Steiner set of G if every vertex of G is contained in a Steiner W-tree of G. The Steiner number s(G) of G is the minimum cardinality of its Steiner sets and any Steiner set of cardinality s(G) is a minimum Steiner set of G. For a minimum Steiner set W of G, a subset T ⊆ W is called a forcing subset for W if W is the unique minimum Steiner set containing T. A forcing subset for W of minimum cardinality is a minimum forcing subset of W. The forcing Steiner number of W, denoted by fₛ(W), is the cardinality of a minimum forcing subset of W. The forcing Steiner number of G, denoted by fₛ(G), is fₛ(G) = min{fₛ(W)}, where the minimum is taken over all minimum Steiner sets W in G. Some general properties satisfied by this concept are studied. The forcing Steiner numbers of certain classes of graphs are determined. It is shown for every pair a, b of integers with 0 ≤ a < b, b ≥ 2, there exists a connected graph G such that fₛ(G) = a and s(G) = b.
Kategorie tematyczne
Wydawca
Rocznik
Tom
31
Numer
1
Strony
171-181
Opis fizyczny
Daty
wydano
2011
otrzymano
2009-02-18
poprawiono
2009-04-24
zaakceptowano
2009-04-27
Twórcy
  • Research Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai - 627 002, India
autor
  • Department of Mathematics, Alagappa Chettiar Govt. College of Engineering & Technology, Karaikudi - 630 004, India
Bibliografia
  • [1] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley, Redwood City, CA, 1990).
  • [2] G. Chartrand and P. Zhang, The forcing geodetic number of a graph, Discuss. Math. Graph Theory 19 (1999) 45-58, doi: 10.7151/dmgt.1084.
  • [3] G. Chartrand and P. Zhang, The forcing dimension of a graph, Mathematica Bohemica 126 (2001) 711-720.
  • [4] G. Chartrand, F. Harary and P. Zhang, On the geodetic number of a graph, Networks 39 (2002) 1-6, doi: 10.1002/net.10007.
  • [5] G. Chartrand, F. Harary and P. Zhang, The Steiner Number of a Graph, Discrete Math. 242 (2002) 41-54.
  • [6] F. Harary, E. Loukakis and C. Tsouros, The geodetic number of a graph, Math. Comput. Modelling 17 (1993) 89-95, doi: 10.1016/0895-7177(93)90259-2.
  • [7] C. Hernando, T. Jiang, M. Mora, I.M. Pelayo and C. Seara, On the Steiner, geodetic and hull numbers of graphs, Discrete Math. 293 (2005) 139-154, doi: 10.1016/j.disc.2004.08.039.
  • [8] I.M. Pelayo, Comment on 'The Steiner number of a graph' by G. Chartrand and P. Zhang, Discrete Math. 242 (2002) 41-54.
  • [9] A.P. Santhakumaran, P. Titus and J. John, On the Connected Geodetic Number of a Graph, J. Combin. Math. Combin. Comput. 69 (2009) 205-218.
  • [10] A.P. Santhakumaran, P. Titus and J. John, The Upper Connected Geodetic Number and Forcing Connected Geodetic Number of a Graph, Discrete Appl. Math. 157 (2009) 1571-1580, doi: 10.1016/j.dam.2008.06.005.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1536
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