A characterization of the corona product of a cycle with some graphs based on its f-chromatic index
Adiwijaya Adiwijaya, A.N.M. Salman, Djoko Suprijanto, Edy Tri Baskoro · AIP conference proceedings · 2012
An f-coloring of graph G(V,E) is a generalized edge-coloring such that every vertex ν in V has at most f(ν) edges colored with a same color. There are many applications of the f-coloring, for instance we can use it in order to solve some scheduling problems and some network design problems. The minimum number of colors needed to f-color G is called an the f-chromatic index of G, denoted by χ′f(G). Any graph G has f-chromatic index equal to Δf(G) or Δf(G)+1, where Δf(G) = maxνϵV{⌈d(ν)/f(ν)⌉}. G is called in the class-1, denoted by G ϵ Cf 1, if χ′f(G) = Δf(G); otherwise G is called in the class-2, denoted by G ϵ Cf 2. In this paper, we show that the corona product of Cn with Sm is in Cf 1. Besides that, we characterize the corona product of Cn with either Wn or Kn based on f-coloring.