On Some Graph Colorings

In this paper three different types of colorings are studied, which are incidence coloring of graphs, acyclic edge coloring and strong edge coloring. We determine the incidence chromatic number of inflation of trees and 3k-cycles and uniform inflation of cycles , K2n, fans and Halin graphs with â–³> 6. We prove that Halin graphs,1-trees and outerplanar graphs satisfy the conjecture presented by N. Alon that the acyclic edge chromatic number of any graph does not exceed its maximum degree plus 2. We also show strong edge chromatic number of two types of regular graphs with high degree and a note on a result of A. C. Burris.