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

Abstract

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The radio antipodal number of a graph G is the smallest integer c such that there exists an assignment f V ( G ) → { 1 , 2 , ... , c } satisfying | f ( u ) - f ( v ) | ≥ 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.

How to cite

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Khennoufa, 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

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  1. Radio labelings of graphs, Bull. Inst. Combin. Appl. 33 (2001), 77–85. (2001) MR1913399
  2. Radio antipodal colorings of cycles, Congr. Numerantium 144 (2000), 129–141. (2000) MR1817928
  3. Radio antipodal colorings of graphs, Math. Bohem. 127 (2002), 57–69. (2002) MR1895247
  4. 10.7151/dmgt.1209, Discuss. Math. Graph Theory 24 (2004), 5–21. (2004) MR2118291DOI10.7151/dmgt.1209
  5. 10.1016/j.disc.2003.11.009, Discrete Math. 283 (2004), 137–144. (2004) MR2061491DOI10.1016/j.disc.2003.11.009
  6. Multi-level distance labelings for paths and cycles, (to appear). (to appear) 

Citations in EuDML Documents

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  1. Yu-Fa Shen, Guo-Ping Zheng, Wen-Jie HeK, Improved upper bounds for nearly antipodal chromatic number of paths
  2. Mustapha Kchikech, Riadh Khennoufa, Olivier Togni, Radio k-labelings for Cartesian products of graphs
  3. Srinivasa Rao Kola, Pratima Panigrahi, Nearly antipodal chromatic number a c ' ( P n ) of the path P n
  4. Mustapha Kchikech, Riadh Khennoufa, Olivier Togni, Linear and cyclic radio k-labelings of trees
  5. Futaba Fujie-Okamoto, Willem Renzema, Ping Zhang, The k -metric colorings of a graph

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