Radio numbers for generalized prism graphs

• Autorzy: Paul Martinez , Juan Ortiz , Maggy Tomova , Cindy Wyels
• Języki publikacji: EN

Abstrakty

EN

A radio labeling is an assignment c:V(G) → N such that every distinct pair of vertices u,v satisfies the inequality d(u,v) + |c(u)-c(v)| ≥ diam(G) + 1. The span of a radio labeling is the maximum value. The radio number of G, rn(G), is the minimum span over all radio labelings of G. Generalized prism graphs, denoted $Z_{n,s}$, s ≥ 1, n ≥ s, have vertex set {(i,j) | i = 1,2 and j = 1,...,n} and edge set {((i,j),(i,j ±1))} ∪ {((1,i),(2,i+σ)) | σ = -⌊(s-1)/2⌋...,0,...,⌊s/2⌋}. In this paper we determine the radio number of $Z_{n,s}$ for s = 1,2 and 3. In the process we develop techniques that are likely to be of use in determining radio numbers of other families of graphs.

Słowa kluczowe

EN

radio number; radio labeling; prism graphs

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: 2011
• Tom: 31
• Numer: 1
• Strony: 45-62

Daty

wydano

2011

otrzymano

2009-04-01

poprawiono

2010-04-01

zaakceptowano

2010-04-06

Twórcy

autor

Paul Martinez

• California State University Channel Islands

autor

Juan Ortiz

• Lehigh University

autor

Maggy Tomova

• The University of Iowa

autor

Cindy Wyels

• California State University Channel Islands

Bibliografia

• [1] G. Chang and D. Kuo, The L(2,1)-labeling problem on graphs, SIAM J. Discrete Math. 9 (1996) 309-316, doi: 10.1137/S0895480193245339.
• [2] G. Chartrand, D. Erwin, P. Zhang and F. Harary, Radio labelings of graphs, Bull. Inst. Combin. Appl. 33 (2001) 77-85.
• [3] G. Chartrand and P. Zhang, Radio colorings of graphs-a survey, Int. J. Comput. Appl. Math. 2 (2007) 237-252.
• [4] W.K. Hale, Frequency assignment: theory and application, Proc. IEEE 68 (1980) 1497-1514, doi: 10.1109/PROC.1980.11899.
• [5] R. Khennoufa and O. Togni, The Radio Antipodal and Radio Numbers of the Hypercube, Ars Combin., in press.
• [6] X. Li, V. Mak and S. Zhou, Optimal radio labellings of complete m-ary trees, Discrete Appl. Math. 158 (2010) 507-515, doi: 10.1016/j.dam.2009.11.014.
• [7] D.D.-F. Liu, Radio number for trees, Discrete Math. 308 (2008) 1153-1164, doi: 10.1016/j.disc.2007.03.066.
• [8] D.D.-F. Liu and M. Xie, Radio numbers of squares of cycles, Congr. Numer. 169 (2004) 101-125.
• [9] D.D.-F. Liu and M. Xie, Radio number for square paths, Ars Combin. 90 (2009) 307-319.
• [10] D.D.-F. Liu and X. Zhu, Multilevel distance labelings for paths and cycles, SIAM J. Discrete Math. 19 (2009) 610-621 (electronic), doi: 10.1137/S0895480102417768.
• [11] P. Zhang, Radio labelings of cycles, Ars Combin. 65 (2002) 21-32.

Identyfikatory

DOI

10.7151/dmgt.1529