Radio antipodal colorings of graphs

Chartrand, Gary, Erwin, David, and Zhang, Ping. "Radio antipodal colorings of graphs." Mathematica Bohemica 127.1 (2002): 57-69. <http://eudml.org/doc/248888>.

@article{Chartrand2002,
abstract = {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 $\mathop \{\mathrm \{a\}c\}(c)$ of a radio antipodal coloring $c$ of $G$ is the maximum color assigned to a vertex of $G$. The radio antipodal chromatic number $\mathop \{\mathrm \{a\}c\}(G)$ of $G$ is $\min \lbrace \mathop \{\mathrm \{a\}c\}(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.},
author = {Chartrand, Gary, Erwin, David, Zhang, Ping},
journal = {Mathematica Bohemica},
keywords = {radio antipodal coloring; radio antipodal chromatic number; distance; radio antipodal coloring; radio antipodal chromatic number; distance},
language = {eng},
number = {1},
pages = {57-69},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Radio antipodal colorings of graphs},
url = {http://eudml.org/doc/248888},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Chartrand, Gary
AU - Erwin, David
AU - Zhang, Ping
TI - Radio antipodal colorings of graphs
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 1
SP - 57
EP - 69
AB - 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 $\mathop {\mathrm {a}c}(c)$ of a radio antipodal coloring $c$ of $G$ is the maximum color assigned to a vertex of $G$. The radio antipodal chromatic number $\mathop {\mathrm {a}c}(G)$ of $G$ is $\min \lbrace \mathop {\mathrm {a}c}(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.
LA - eng
KW - radio antipodal coloring; radio antipodal chromatic number; distance; radio antipodal coloring; radio antipodal chromatic number; distance
UR - http://eudml.org/doc/248888
ER -