Discussiones Mathematicae Graph Theory 31(3) (2011) 429-439
doi: 10.7151/dmgt.1556

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ADJACENT VERTEX DISTINGUISHING EDGE-COLORINGS OF PLANAR GRAPHS WITH GIRTH AT LEAST SIX

Yuehua Bu1, Ko-Wei Lih2 and Weifan Wang1

1Department of Mathematics
Zhejiang Normal University
Zhejiang, Jinhua 321004, China

2Institute of Mathematics
Academia Sinica
Nankang, Taipei 11529, Taiwan
e-mail: yhbu@zjnu.cn
makwlih@sinica.edu.tw
wwf@zjnu.cn

Abstract

An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring o G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ′a(G). We prove that χ′a(G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in  [Z. Zhang, L. Liu, and J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett., 15 (2002) 623-626.]

Keywords: edge-coloring, vertex-distinguishing, planar graph.

2010 Mathematics Subject Classification: 05C15.

References

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Received 18 November 2009
Revised 27 March 2010
Accepted 30 April 2010