Geodesic
Radio number for some thorn graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 2, pp. 201-222.

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

For a graph G and any two vertices u and v in G, let d(u,v) denote the distance between u and v and let diam(G) be the diameter of G. A multilevel distance labeling (or radio labeling) for G is a function f that assigns to each vertex of G a positive integer such that for any two distinct vertices u and v, d(u,v) + |f(u) - f(v)| ≥ diam(G) + 1. The largest integer in the range of f is called the span of f and is denoted span(f). The radio number of G, denoted rn(G), is the minimum span of any radio labeling for G. A thorn graph is a graph obtained from a given graph by attaching new terminal vertices to the vertices of the initial graph. In this paper the radio numbers for two classes of thorn graphs are determined: the caterpillar obtained from the path Pₙ by attaching a new terminal vertex to each non-terminal vertex and the thorn star S_n,k obtained from the star Sₙ by attaching k new terminal vertices to each terminal vertex of the star.
Keywords: multilevel distance labeling, radio number, caterpillar, diameter 
@article{DMGT_2010_30_2_a1,
     author = {Marinescu-Ghemeci, Ruxandra},
     title = {Radio number for some thorn graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {201--222},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a1/}
}
TY  - JOUR
AU  - Marinescu-Ghemeci, Ruxandra
TI  - Radio number for some thorn graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2010
SP  - 201
EP  - 222
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a1/
LA  - en
ID  - DMGT_2010_30_2_a1
ER  - 
%0 Journal Article
%A Marinescu-Ghemeci, Ruxandra
%T Radio number for some thorn graphs
%J Discussiones Mathematicae. Graph Theory
%D 2010
%P 201-222
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a1/
%G en
%F DMGT_2010_30_2_a1
Marinescu-Ghemeci, Ruxandra. Radio number for some thorn graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 2, pp. 201-222. http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a1/

[1] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley Pub. Co., 1990).

[2] G. Chartrand, D. Erwin, F. Harary and P. Zhang, Radio labelings of graphs, Bull. Inst. Combin. Appl. 33 (2001) 77-85.

[3] G. Chartrand, D. Erwin and P. Zhang, A graph labeling problem suggested by FM channel restrictions, Bull. Inst. Combin. Appl. 43 (2005) 43-57.

[4] J.A. Gallian, A dynamic survey of graph labelings, Electronic J. Combinatorics 14 (2007) #DS6.

[5] I. Gutman, Distance of thorny graphs, Publ. Inst. Math. (Beograd) 63 (1998) 31-36.

[6] W.K. Hale, Frequency assignment: theory and applications, Proc. IEEE 68 (1980) 1497-1514, doi: 10.1109/PROC.1980.11899.

[7] D. Liu, Radio number for trees, Discrete Math. 308 (2008) 1153-1164, doi: 10.1016/j.disc.2007.03.066.

[8] D. Liu and X. Zhu, Multilevel distance labelings for paths and cycles, SIAM J. Discrete Math. 19 (2005) 610-621, doi: 10.1137/S0895480102417768.

[9] M.T. Rahim and I. Tomescu, Multilevel distance labelings for helm graphs, Ars Combinatoria, to appear.