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## Discussiones Mathematicae Graph Theory

2010 | 30 | 1 | 55-73
Tytuł artykułu

### The edge geodetic number and Cartesian product of graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a nontrivial connected graph G = (V(G),E(G)), a set S⊆ V(G) is called an edge geodetic set of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g₁(G) of G is the minimum order of its edge geodetic sets. Bounds for the edge geodetic number of Cartesian product graphs are proved and improved upper bounds are determined for a special class of graphs. Exact values of the edge geodetic number of Cartesian product are obtained for several classes of graphs. Also we obtain a necessary condition of G for which g₁(G ☐ K₂) = g₁(G).
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EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
55-73
Opis fizyczny
Daty
wydano
2010
otrzymano
2008-05-28
poprawiono
2008-12-11
zaakceptowano
2009-01-21
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, (2007), 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 and P. Zhang, Introduction to Graph Theory (Tata McGraw-Hill Edition, New Delhi, 2006).
• [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] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (Wiley-Interscience, New York, 2000).
• [7] A.P. Santhakumaran and J. John, Edge geodetic number of a graph, J. Discrete Math. Sciences & Cryptography 10 (2007) 415-432.
Typ dokumentu
Bibliografia
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