On graphs with a unique minimum hull set

• Autorzy: Gary Chartrand , Ping Zhang
• Języki publikacji: EN

Abstrakty

EN

We show that for every integer k ≥ 2 and every k graphs G₁,G₂,...,Gₖ, there exists a hull graph with k hull vertices v₁,v₂,...,vₖ such that link $L(v_i) = G_i$ for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a,b of integers with a ≥ 2 and b ≥ 0 is realizable as the hull number and forcing geodetic number of a hull graph.

Słowa kluczowe

EN

geodetic set; geodetic number; convex hull; hull set; hull number; hull graph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 31-42

Daty

wydano

2001

otrzymano

2000-03-08

poprawiono

2001-03-14

Twórcy

autor

Gary Chartrand

• Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA

autor

Ping Zhang

• Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA

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, to appear.
• [3] G. Chartrand, F. Harary and P. Zhang, On the hull number of a graph, Ars Combin. 57 (2000) 129-138.
• [4] G. Chartrand and P. Zhang, The geodetic number of an oriented graph, European J. Combin. 21 (2) (2000) 181-189, doi: 10.1006/eujc.1999.0301.
• [5] 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.
• [6] G. Chartrand and P. Zhang, The forcing hull number of a graph, J. Combin. Math. Combin. Comput. to appear.
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• [10] H.M. Mulder, The Interval Function of a Graph (Methematisch Centrum, Amsterdam, 1980).
• [11] H.M. Mulder, The expansion procedure for graphs, in: Contemporary Methods in Graph Theory ed., R. Bodendiek (Wissenschaftsverlag, Mannheim, 1990) 459-477.
• [12] L. Nebeský, A characterization of the interval function of a connected graph, Czech. Math. J. 44 (119) (1994) 173-178.
• [13] L. Nebeský, Characterizing of the interval function of a connected graph, Math. Bohem. 123 (1998) 137-144.

Identyfikatory

DOI

10.7151/dmgt.1131