Equitable Coloring of Mycielskian of Some graphs

Abstract

In a search for triangle-free graphs with arbitrarily large chromaticnumbers, Mycielski developed a graph transformation that transformsa graph G into a new graph (G), we now call the Mycielskian ofG, which has the same clique number as G and whose chromatic numberequals (G)+1. This paper presents exact values of the equitable chromaticnumber = for the Mycielski's graph of complete graphs (Kn),the Mycielski's graph of cycles (Cn), the Mycielski's graph of paths(Pn), the Mycielski's graph of Helm graphs (Hn) and the Mycielski'sgraph of Gear graphs (Gn).