Point-distinguishing chromatic index of the union of paths

Xiang'en Chen

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 3, page 629-640
  • ISSN: 0011-4642

Abstract

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Let G be a simple graph. For a general edge coloring of a graph G (i.e., not necessarily a proper edge coloring) and a vertex v of G , denote by S ( v ) the set (not a multiset) of colors used to color the edges incident to v . For a general edge coloring f of a graph G , if S ( u ) ≠ S ( v ) for any two different vertices u and v of G , then we say that f is a point-distinguishing general edge coloring of G . The minimum number of colors required for a point-distinguishing general edge coloring of G , denoted by χ 0 ( G ) , is called the point-distinguishing chromatic index of G . In this paper, we determine the point-distinguishing chromatic index of the union of paths and propose a conjecture.

How to cite

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Chen, Xiang'en. "Point-distinguishing chromatic index of the union of paths." Czechoslovak Mathematical Journal 64.3 (2014): 629-640. <http://eudml.org/doc/262192>.

@article{Chen2014,
abstract = {Let $G$ be a simple graph. For a general edge coloring of a graph $G$ (i.e., not necessarily a proper edge coloring) and a vertex $v$ of $G$, denote by $S(v)$ the set (not a multiset) of colors used to color the edges incident to $v$. For a general edge coloring $f$ of a graph $G$, if $S(u)\ne S(v)$ for any two different vertices $u$ and $v$ of $G$, then we say that $f$ is a point-distinguishing general edge coloring of $G$. The minimum number of colors required for a point-distinguishing general edge coloring of $G$, denoted by $\chi _\{0\}(G)$, is called the point-distinguishing chromatic index of $G$. In this paper, we determine the point-distinguishing chromatic index of the union of paths and propose a conjecture.},
author = {Chen, Xiang'en},
journal = {Czechoslovak Mathematical Journal},
keywords = {general edge coloring; point-distinguishing general edge coloring; point-distinguishing chromatic index; general edge coloring; point-distinguishing general edge coloring; point-distinguishing chromatic index},
language = {eng},
number = {3},
pages = {629-640},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Point-distinguishing chromatic index of the union of paths},
url = {http://eudml.org/doc/262192},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Chen, Xiang'en
TI - Point-distinguishing chromatic index of the union of paths
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 3
SP - 629
EP - 640
AB - Let $G$ be a simple graph. For a general edge coloring of a graph $G$ (i.e., not necessarily a proper edge coloring) and a vertex $v$ of $G$, denote by $S(v)$ the set (not a multiset) of colors used to color the edges incident to $v$. For a general edge coloring $f$ of a graph $G$, if $S(u)\ne S(v)$ for any two different vertices $u$ and $v$ of $G$, then we say that $f$ is a point-distinguishing general edge coloring of $G$. The minimum number of colors required for a point-distinguishing general edge coloring of $G$, denoted by $\chi _{0}(G)$, is called the point-distinguishing chromatic index of $G$. In this paper, we determine the point-distinguishing chromatic index of the union of paths and propose a conjecture.
LA - eng
KW - general edge coloring; point-distinguishing general edge coloring; point-distinguishing chromatic index; general edge coloring; point-distinguishing general edge coloring; point-distinguishing chromatic index
UR - http://eudml.org/doc/262192
ER -

References

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