| Title:
|
A note on radio antipodal colourings of paths (English) |
| Author:
|
Khennoufa, Riadh |
| Author:
|
Togni, Olivier |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
277-282 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The radio antipodal number of a graph $G$ is the smallest integer $c$ such that there exists an assignment $f\: V(G)\rightarrow \lbrace 1,2,\ldots ,c\rbrace $ satisfying $|f(u)-f(v)|\ge D-d(u,v)$ for every two distinct vertices $u$ and $v$ of $G$, where $D$ is the diameter of $G$. In this note we determine the exact value of the antipodal number of the path, thus answering the conjecture given in [G. Chartrand, D. Erwin and P. Zhang, Math. Bohem. 127 (2002), 57–69]. We also show the connections between this colouring and radio labelings. (English) |
| Keyword:
|
radio antipodal colouring |
| Keyword:
|
radio number |
| Keyword:
|
distance labeling |
| MSC:
|
05C12 |
| MSC:
|
05C15 |
| MSC:
|
05C78 |
| idZBL:
|
Zbl 1110.05033 |
| idMR:
|
MR2164657 |
| DOI:
|
10.21136/MB.2005.134100 |
| . |
| Date available:
|
2009-09-24T22:21:08Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134100 |
| . |
| Reference:
|
[1] G. Chartrand, D. Erwin, F. Harary, P. Zhang: Radio labelings of graphs.Bull. Inst. Combin. Appl. 33 (2001), 77–85. MR 1913399 |
| Reference:
|
[2] G. Chartrand, D. Erwin, P. Zhang: Radio antipodal colorings of cycles.Congr. Numerantium 144 (2000), 129–141. MR 1817928 |
| Reference:
|
[3] G. Chartrand, D. Erwin, P. Zhang: Radio antipodal colorings of graphs.Math. Bohem. 127 (2002), 57–69. MR 1895247 |
| Reference:
|
[4] G. Chartrand, L. Nebeský, P. Zhang: Radio $k$-colorings of paths.Discuss. Math. Graph Theory 24 (2004), 5–21. MR 2118291, 10.7151/dmgt.1209 |
| Reference:
|
[5] D. Kuo, J.-H. Yan: On $L(2,1)$-labelings of Cartesian products of paths and cycles.Discrete Math. 283 (2004), 137–144. MR 2061491, 10.1016/j.disc.2003.11.009 |
| Reference:
|
[6] D. Liu, X. Zhu: Multi-level distance labelings for paths and cycles.(to appear). |
| . |
