AVD Proper Edge-Coloring of some Cycle Related Graphs

Abstract

The adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for a proper edge-coloring of G, in which no two adjacent vertices are incident to edges colored with the same set of colors. The minimum number of colors required for an adjacent vertex-distinguishing proper edge-coloring of G is called the adjacent vertex-distinguishing proper edge-chromatic index. In this paper, I compute adjacent vertex-distinguishing proper edge-chromatic index of Anti-prism, sunflower graph, double sunflower graph, triangular winged prism, rectangular winged prism and Polygonal snake graph.

Keywords

• Edge coloring
• AVD proper edge-coloring
• cycle;

References

1. 1. Axenovich, M.,Harant,J,Przyby-lo, J.,Sotak, R., Voigt, M., Weidelich, J., A note on adjacent vertex distinguishing colorings of graphs, Discrete Applied Mathematics, 205,(2016),1-7 2. Balister, P.N., Gyori, E., Lehel, J., Schelp, R.H., Adjacent vertex distinguishing edge-coloring, SIAM Journal on Discrete Mathematics, 21(1), (2007), 237-250.