PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Discussiones Mathematicae Graph Theory

2010 | 30 | 4 | 687-700
Tytuł artykułu

### The geodetic number of strong product graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For two vertices u and v of a connected graph G, the set $I_G[u,v]$ consists of all those vertices lying on u-v geodesics in G. Given a set S of vertices of G, the union of all sets $I_G[u,v]$ for u,v ∈ S is denoted by $I_G[S]$. A set S ⊆ V(G) is a geodetic set if $I_G[S] = V(G)$ and the minimum cardinality of a geodetic set is its geodetic number g(G) of G. Bounds for the geodetic number of strong product graphs are obtainted and for several classes improved bounds and exact values are obtained.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
687-700
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-10-29
poprawiono
2010-02-27
zaakceptowano
2010-03-10
Twórcy
autor
• Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai - 627 002, India
autor
• Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai - 627 002, India
Bibliografia
• [1] B. Bresar, S. Klavžar and A.T. Horvat, On the geodetic number and related metric sets in Cartesian product graphs, Discrete Math. 308 (2008) 5555-5561, doi: 10.1016/j.disc.2007.10.007.
• [2] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley, Redwood City, CA, 1990).
• [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, F. Harary, H.C. Swart and P. Zhang, Geodomination in Graphs, Bulletin of the ICA 31 (2001) 51-59.
• [5] G. Chartrand and P. Zhang, Introduction to Graph Theory (Tata McGraw-Hill Edition, New Delhi, 2006).
• [6] F. Harary, E. Loukakis and C. Tsouros, The geodetic number of a graph, Mathl. Comput. Modeling 17 (1993) 89-95, doi: 10.1016/0895-7177(93)90259-2.
• [7] F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000) 201-213.
• [8] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (Wiley-Interscience, New York, 2000).
• [9] A.P. Santhakumaran and S.V. Ullas Chandran, The hull number of strong product of graphs, (communicated).
Typ dokumentu
Bibliografia
Identyfikatory