# The algorithm for adjacent vertex distinguishing proper edge coloring of graphs

@article{Li2015TheAF,
title={The algorithm for adjacent vertex distinguishing proper edge coloring of graphs},
author={Jingwen Li and Tengyun Hu and Fei Wen},
journal={Discret. Math. Algorithms Appl.},
year={2015},
volume={7},
pages={1550044:1-1550044:13}
}
• Published 1 December 2015
• Mathematics
• Discret. Math. Algorithms Appl.
An adjacent vertex distinguishing proper edge coloring of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meet the same set of colors. The minimum number of colors is called adjacent vertex distinguishing proper edge chromatic number of G. In this paper, we present a new heuristic intelligent algorithm to calculate the adjacent vertex distinguishing proper edge chromatic number of graphs. To be exact, the algorithm establishes two objective subfunctions and a…
1 Citations

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## References

SHOWING 1-10 OF 21 REFERENCES
Vertex-distinguishing proper edge-colorings
• Mathematics
J. Graph Theory
• 1997
An edge-coloring is called vertex-distinguishing if every two distinct vertices are incident to different sets of colored edges. The minimum number of colors required for a vertex-distinguishing
• Mathematics
SIAM J. Discret. Math.
• 2007
The minimum number of colors required to give an adjacent vertex distinguishing edge-coloring of a simple graph G is proved and a weaker result of the form $\chi^\prime_a(G)=\Delta(G)+O(\log k)$.
Adjacent vertex distinguishing edge-colorings of graphs with smaller maximum average degree
• Mathematics
J. Comb. Optim.
• 2010
This paper proves that the minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is χ′a(G)≤Δ+2, if and only if G contains adjacent vertices of maximum degree.
Strong edge colorings of graphs
• Mathematics
Discret. Math.
• 1996
ADJACENT VERTEX DISTINGUISHING TOTAL COLORING OF GRAPHS WITH LOWER AVERAGE DEGREE
• Mathematics
• 2008
An adjacent vertex distinguishing total coloring of a graph $G$ is a proper total coloring of $G$ such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number