Geodesic
On graphs with a unique minimum hull set
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 31-42.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: geodetic set, geodetic number, convex hull, hull set, hull number, hull graph 
@article{DMGT_2001_21_1_a2,
     author = {Chartrand, Gary and Zhang, Ping},
     title = {On graphs with a unique minimum hull set},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {31--42},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a2/}
}
TY  - JOUR
AU  - Chartrand, Gary
AU  - Zhang, Ping
TI  - On graphs with a unique minimum hull set
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2001
SP  - 31
EP  - 42
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a2/
LA  - en
ID  - DMGT_2001_21_1_a2
ER  - 
%0 Journal Article
%A Chartrand, Gary
%A Zhang, Ping
%T On graphs with a unique minimum hull set
%J Discussiones Mathematicae. Graph Theory
%D 2001
%P 31-42
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a2/
%G en
%F DMGT_2001_21_1_a2
Chartrand, Gary; Zhang, Ping. On graphs with a unique minimum hull set. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 31-42. http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a2/

[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.

[7] M.G. Everett and S.B. Seidman, The hull number of a graph, Discrete Math. 57 (1985) 217-223, doi: 10.1016/0012-365X(85)90174-8.

[8] F. Harary and J. Nieminen, Convexity in graphs, J. Differential Geom. 16 (1981) 185-190.

[9] F. Harary, E. Loukakis and C. Tsouros, The geodetic number of a graph, Mathl. Comput. Modelling. 17 (11) (1993) 89-95, doi: 10.1016/0895-7177(93)90259-2.

[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.