# Radio number for some thorn graphs

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 2, page 201-222
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topRuxandra Marinescu-Ghemeci. "Radio number for some thorn graphs." Discussiones Mathematicae Graph Theory 30.2 (2010): 201-222. <http://eudml.org/doc/271026>.

@article{RuxandraMarinescu2010,

abstract = {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.},

author = {Ruxandra Marinescu-Ghemeci},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {multilevel distance labeling; radio number; caterpillar; diameter},

language = {eng},

number = {2},

pages = {201-222},

title = {Radio number for some thorn graphs},

url = {http://eudml.org/doc/271026},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Ruxandra Marinescu-Ghemeci

TI - Radio number for some thorn graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 2

SP - 201

EP - 222

AB - 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.

LA - eng

KW - multilevel distance labeling; radio number; caterpillar; diameter

UR - http://eudml.org/doc/271026

ER -

## References

top- [1] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley Pub. Co., 1990). Zbl0688.05017
- [2] G. Chartrand, D. Erwin, F. Harary and P. Zhang, Radio labelings of graphs, Bull. Inst. Combin. Appl. 33 (2001) 77-85. Zbl0989.05102
- [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. Zbl1066.05125
- [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. Zbl0942.05021
- [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. Zbl1133.05090
- [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. Zbl1095.05033
- [9] M.T. Rahim and I. Tomescu, Multilevel distance labelings for helm graphs, Ars Combinatoria, to appear.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.