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## Discussiones Mathematicae Graph Theory

2011 | 31 | 4 | 611-624
Tytuł artykułu

### On the forcing geodetic and forcing steiner numbers of a graph

Autorzy
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. The geodetic number g(G) and the forcing geodetic number f(G) of a graph G are defined in [2]. It is proved in [6] that there is no relationship between the geodetic number and the Steiner number of a graph so that there is no relationship between the forcing geodetic number and the forcing Steiner number of a graph. We give realization results for various possibilities of these four parameters.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
611-624
Opis fizyczny
Daty
wydano
2011
otrzymano
2009-06-08
poprawiono
2010-07-23
zaakceptowano
2010-07-28
Twórcy
autor
• Research Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai-627 002, India
autor
• Department of Mathematics, Government College of Engineering, Tirunelveli - 627 007, 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, F. Harary and P. Zhang, On the geodetic number of a graph, Networks 39 (2002) 1-6, doi: 10.1002/net.10007.
• [4] G. Chartrand and P. Zhang, The Steiner number of a graph, Discrete Math. 242 (2002) 41-54, doi: 10.1016/S0012-365X(00)00456-8.
• [5] F. Harary, E. Loukakis and C. Tsouros, The geodetic number of a graph, Math. Comput. Modeling 17 (1993) 89-95, doi: 10.1016/0895-7177(93)90259-2.
• [6] I.M. Pelayo, Comment on 'The Steiner number of a graph' by G. Chartrand and P. Zhang, Discrete Math. 242 (2002) 41-54.
• [7] A.P. Santhakumaran, P. Titus and J. John, On the connected geodetic number of a graph, J. Combin. Math. Combin. Comput. 69 (2009) 219-229.
• [8] A.P. Santhakumaran, P. Titus and J. John, The upper connected geodetic number and forcing connected geodetic number of a graph, Discrete Appl. Math. 159 (2009) 1571-1580, doi: 10.1016/j.dam.2008.06.005.
Typ dokumentu
Bibliografia
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