## Abstract

A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv ∈ E(G). The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by X′ _{Aa}(G), is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.

Original language | English |
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Pages (from-to) | 439-452 |

Number of pages | 14 |

Journal | Applied Mathematics |

Volume | 26 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 2011 |

## Scopus Subject Areas

- Applied Mathematics

## User-Defined Keywords

- Adjacent strong edge coloring
- adjacent vertex-distinguishing acyclic edge coloring