# A note on radio antipodal colourings of paths

Riadh Khennoufa; Olivier Togni

Mathematica Bohemica (2005)

- Volume: 130, Issue: 3, page 277-282
- ISSN: 0862-7959

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topKhennoufa, Riadh, and Togni, Olivier. "A note on radio antipodal colourings of paths." Mathematica Bohemica 130.3 (2005): 277-282. <http://eudml.org/doc/249599>.

@article{Khennoufa2005,

abstract = {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.},

author = {Khennoufa, Riadh, Togni, Olivier},

journal = {Mathematica Bohemica},

keywords = {radio antipodal colouring; radio number; distance labeling; radio number; distance labeling},

language = {eng},

number = {3},

pages = {277-282},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A note on radio antipodal colourings of paths},

url = {http://eudml.org/doc/249599},

volume = {130},

year = {2005},

}

TY - JOUR

AU - Khennoufa, Riadh

AU - Togni, Olivier

TI - A note on radio antipodal colourings of paths

JO - Mathematica Bohemica

PY - 2005

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 130

IS - 3

SP - 277

EP - 282

AB - 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.

LA - eng

KW - radio antipodal colouring; radio number; distance labeling; radio number; distance labeling

UR - http://eudml.org/doc/249599

ER -

## References

top- Radio labelings of graphs, Bull. Inst. Combin. Appl. 33 (2001), 77–85. (2001) MR1913399
- Radio antipodal colorings of cycles, Congr. Numerantium 144 (2000), 129–141. (2000) MR1817928
- Radio antipodal colorings of graphs, Math. Bohem. 127 (2002), 57–69. (2002) MR1895247
- 10.7151/dmgt.1209, Discuss. Math. Graph Theory 24 (2004), 5–21. (2004) MR2118291DOI10.7151/dmgt.1209
- 10.1016/j.disc.2003.11.009, Discrete Math. 283 (2004), 137–144. (2004) MR2061491DOI10.1016/j.disc.2003.11.009
- Multi-level distance labelings for paths and cycles, (to appear). (to appear)

## Citations in EuDML Documents

top- Yu-Fa Shen, Guo-Ping Zheng, Wen-Jie HeK, Improved upper bounds for nearly antipodal chromatic number of paths
- Mustapha Kchikech, Riadh Khennoufa, Olivier Togni, Radio k-labelings for Cartesian products of graphs
- Srinivasa Rao Kola, Pratima Panigrahi, Nearly antipodal chromatic number $a{c}^{\text{'}}\left({P}_{n}\right)$ of the path ${P}_{n}$
- Mustapha Kchikech, Riadh Khennoufa, Olivier Togni, Linear and cyclic radio k-labelings of trees
- Futaba Fujie-Okamoto, Willem Renzema, Ping Zhang, The $k$-metric colorings of a graph

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