The geodetic number of strong product graphs

• Autorzy: A.P. Santhakumaran , S.V. Ullas Chandran
• 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

geodetic number; extreme vertex; extreme geodesic graph; open geodetic number; double domination number

Kategorie tematyczne

• 05C12: Distance in graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 4
• Strony: 687-700

Daty

wydano

2010

otrzymano

2009-10-29

poprawiono

2010-02-27

zaakceptowano

2010-03-10

Twórcy

autor

A.P. Santhakumaran

• Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai - 627 002, India

autor

S.V. Ullas Chandran

• Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai - 627 002, India

Bibliografia

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• [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).

Identyfikatory

DOI

10.7151/dmgt.1523