Radio number for some thorn graphs

• Autorzy: Ruxandra Marinescu-Ghemeci
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

multilevel distance labeling; radio number; caterpillar; diameter

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C78: Graph labelling (graceful graphs, bandwidth, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 2
• Strony: 201-222

Daty

wydano

2010

otrzymano

2008-11-12

poprawiono

2009-06-08

zaakceptowano

2009-06-08

Twórcy

autor

Ruxandra Marinescu-Ghemeci

• Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei, 14, 010014 Bucharest, Romania

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgt.1487