Geodesic
Radio antipodal colorings of graphs
Mathematica Bohemica, Tome 127 (2002) no. 1, pp. 57-69
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A radio antipodal coloring of a connected graph $G$ with diameter $d$ is an assignment of positive integers to the vertices of $G$, with $x \in V(G)$ assigned $c(x)$, such that \[ d(u, v) + |c(u) -c(v)| \ge d \] for every two distinct vertices $u$, $v$ of $G$, where $d(u, v)$ is the distance between $u$ and $v$ in $G$. The radio antipodal coloring number $\mathop {\mathrm ac}(c)$ of a radio antipodal coloring $c$ of $G$ is the maximum color assigned to a vertex of $G$. The radio antipodal chromatic number $\mathop {\mathrm ac}(G)$ of $G$ is $\min \lbrace \mathop {\mathrm ac}(c)\rbrace $ over all radio antipodal colorings $c$ of $G$. Radio antipodal chromatic numbers of paths are discussed and upper and lower bounds are presented. Furthermore, upper and lower bounds for radio antipodal chromatic numbers of graphs are given in terms of their diameter and other invariants.
A radio antipodal coloring of a connected graph $G$ with diameter $d$ is an assignment of positive integers to the vertices of $G$, with $x \in V(G)$ assigned $c(x)$, such that \[ d(u, v) + |c(u) -c(v)| \ge d \] for every two distinct vertices $u$, $v$ of $G$, where $d(u, v)$ is the distance between $u$ and $v$ in $G$. The radio antipodal coloring number $\mathop {\mathrm ac}(c)$ of a radio antipodal coloring $c$ of $G$ is the maximum color assigned to a vertex of $G$. The radio antipodal chromatic number $\mathop {\mathrm ac}(G)$ of $G$ is $\min \lbrace \mathop {\mathrm ac}(c)\rbrace $ over all radio antipodal colorings $c$ of $G$. Radio antipodal chromatic numbers of paths are discussed and upper and lower bounds are presented. Furthermore, upper and lower bounds for radio antipodal chromatic numbers of graphs are given in terms of their diameter and other invariants.
DOI : 10.21136/MB.2002.133978
Classification : 05C12, 05C15, 05C78
Keywords: radio antipodal coloring; radio antipodal chromatic number; distance 
@article{10_21136_MB_2002_133978,
     author = {Chartrand, Gary and Erwin, David and Zhang, Ping},
     title = {Radio antipodal colorings of graphs},
     journal = {Mathematica Bohemica},
     pages = {57--69},
     year = {2002},
     volume = {127},
     number = {1},
     doi = {10.21136/MB.2002.133978},
     mrnumber = {1895247},
     zbl = {0995.05056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2002.133978/}
}
TY  - JOUR
AU  - Chartrand, Gary
AU  - Erwin, David
AU  - Zhang, Ping
TI  - Radio antipodal colorings of graphs
JO  - Mathematica Bohemica
PY  - 2002
SP  - 57
EP  - 69
VL  - 127
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2002.133978/
DO  - 10.21136/MB.2002.133978
LA  - en
ID  - 10_21136_MB_2002_133978
ER  - 
%0 Journal Article
%A Chartrand, Gary
%A Erwin, David
%A Zhang, Ping
%T Radio antipodal colorings of graphs
%J Mathematica Bohemica
%D 2002
%P 57-69
%V 127
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2002.133978/
%R 10.21136/MB.2002.133978
%G en
%F 10_21136_MB_2002_133978
Chartrand, Gary; Erwin, David; Zhang, Ping. Radio antipodal colorings of graphs. Mathematica Bohemica, Tome 127 (2002) no. 1, pp. 57-69. doi: 10.21136/MB.2002.133978

[1] G. Chartrand, D. Erwin, F. Harary, P. Zhang: Radio labelings of graphs. Bull. Inst. Combin. Appl. 33 (2001), 77–85. | MR

[2] G. Chartrand, D. Erwin, P. Zhang: Don’t touch that dial! A graph labeling problem suggested by FM channel restrictions. Preprint. | MR

[3] G. Chartrand, L. Lesniak: Graphs & Digraphs, third edition. Chapman & Hall, New York, 1996. | MR

Cité par Sources :