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Discussiones Mathematicae Graph Theory

2012 | 32 | 1 | 109-119
Tytuł artykułu

Double geodetic number of a graph

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x,y in G there exist vertices u,v ∈ S such that x,y ∈ I[u,v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic of cardinality dg(G) is called dg-set of G. The double geodetic numbers of certain standard graphs are obtained. It is shown that for positive integers r,d such that r < d ≤ 2r and 3 ≤ a ≤ b there exists a connected graph G with rad G = r, diam G = d, g(G) = a and dg(G) = b. Also, it is proved that for integers n, d ≥ 2 and l such that 3 ≤ k ≤ l ≤ n and n-d-l+1 ≥ 0, there exists a graph G of order n diameter d, g(G) = k and dg(G) = l.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
109-119
Opis fizyczny
Daty
wydano
2012
otrzymano
2010-06-30
poprawiono
2011-01-17
zaakceptowano
2011-02-01
Twórcy
autor
• Department of Mathematics, St.Xavier's College (Autonomous), Palayamkottai - 627 002, India
autor
• Department of Mathematics, C.S.I. Institute of Technology, Thovalai - 629 302, India
Bibliografia
• [1] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley, Redwood City, CA, 1990).
• [2] G. Chartrand, F. Harary and P. Zhang, On the geodetic number of a graph, Networks 39 (2002) 1-6, doi: 10.1002/net.10007.
• [3] G. Chartrand, F. Harary, H.C. Swart and P. Zhang, Geodomination in graphs, Bulletin ICA 31 (2001) 51-59.
• [4] F. Harary, Graph Theory (Addision-Wesely, 1969).
• [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] R. Muntean and P. Zhang, On geodomonation in graphs, Congr. Numer. 143 (2000) 161-174.
• [7] P.A. Ostrand, Graphs with specified radius and diameter, Discrete Math. 4 (1973) 71-75, doi: 10.1016/0012-365X(73)90116-7.
Typ dokumentu
Bibliografia
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