Nearly antipodal chromatic number $a{c}^{\text{'}}\left(P_n\right)$ of the path $P_n$

Kola, Srinivasa Rao, and Panigrahi, Pratima. "Nearly antipodal chromatic number $ac^{\prime }(P_n)$ of the path $P_n$." Mathematica Bohemica 134.1 (2009): 77-86. <http://eudml.org/doc/38075>.

@article{Kola2009,
abstract = {Chartrand et al. (2004) have given an upper bound for the nearly antipodal chromatic number $ac^\{\prime \}(P_n)$ as $\binom\{n-2\}\{2\}+2$ for $n \ge 9$ and have found the exact value of $ac^\{\prime \}(P_n)$ for $n=5,6,7,8$. Here we determine the exact values of $ac^\{\prime \}(P_n)$ for $n \ge 8$. They are $2p^2-6p+8$ for $n=2p$ and $2p^2-4p+6$ for $n=2p+1$. The exact value of the radio antipodal number $ac(P_n)$ for the path $P_n$ of order $n$ has been determined by Khennoufa and Togni in 2005 as $2p^2-2p+3$ for $n=2p+1$ and $2p^2-4p+5$ for $n=2p$. Although the value of $ac(P_n)$ determined there is correct, we found a mistake in the proof of the lower bound when $n=2p$ (Theorem $6$). However, we give an easy observation which proves this lower bound.},
author = {Kola, Srinivasa Rao, Panigrahi, Pratima},
journal = {Mathematica Bohemica},
keywords = {radio $k$-coloring; span; radio $k$-chromatic number; radio -coloring; span; radio -chromatic number},
language = {eng},
number = {1},
pages = {77-86},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nearly antipodal chromatic number $ac^\{\prime \}(P_n)$ of the path $P_n$},
url = {http://eudml.org/doc/38075},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Kola, Srinivasa Rao
AU - Panigrahi, Pratima
TI - Nearly antipodal chromatic number $ac^{\prime }(P_n)$ of the path $P_n$
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 1
SP - 77
EP - 86
AB - Chartrand et al. (2004) have given an upper bound for the nearly antipodal chromatic number $ac^{\prime }(P_n)$ as $\binom{n-2}{2}+2$ for $n \ge 9$ and have found the exact value of $ac^{\prime }(P_n)$ for $n=5,6,7,8$. Here we determine the exact values of $ac^{\prime }(P_n)$ for $n \ge 8$. They are $2p^2-6p+8$ for $n=2p$ and $2p^2-4p+6$ for $n=2p+1$. The exact value of the radio antipodal number $ac(P_n)$ for the path $P_n$ of order $n$ has been determined by Khennoufa and Togni in 2005 as $2p^2-2p+3$ for $n=2p+1$ and $2p^2-4p+5$ for $n=2p$. Although the value of $ac(P_n)$ determined there is correct, we found a mistake in the proof of the lower bound when $n=2p$ (Theorem $6$). However, we give an easy observation which proves this lower bound.
LA - eng
KW - radio $k$-coloring; span; radio $k$-chromatic number; radio -coloring; span; radio -chromatic number
UR - http://eudml.org/doc/38075
ER -