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.