ON PALETTE INDEX OF UNICYCLE AND BICYCLE GRAPHS - Ghazaryan, A.B. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2019)
Given a proper edge coloring φ of a graph G , we define the palette S_G ( u, φ) of a vertex u V(G) as the set of all colors appearing on edges incident with u . The palette index s (G) of G is the minimum number of distinct palettes occurring in a proper edge coloring of G . In this paper we give an upper bound on the palette index of a graph G in terms of cyclomatic number cyc(G) of G and maximum degree Δ (G) of G . We also give a sharp upper bound for the palette index of unicycle and bicycle graphs.