EQUITABLE TOTAL COLORING OF SOME CLASS TREES AND MERGING OF CYCLE

An equitable total coloring (χ′′et) of a graph was introduced by Fu in 1994. He gave the conjecture that for any simple graph G the condition χ′′ et(G) ≤ ∆(G) + 2 holds. The graph G = (V, E) is called equitably total k–colorable if the vertex set and edge set of the graph can be partitioned into k non-empty independent sets T1, . . . , Tk such that |Ti| − |Tj | ≤ 1 for every i and j. In this paper we examine and establish equitable total coloring of some trees and merging of cycles.