ABSTRACT
In this work we introduce the concepts of absolute equitable total coloring and graph composition. We prove that for , if , there is a connected k regular graph with n vertices that admits a absolute equitable total coloring, with at most Delta + 2 colors. This result shows that there is a relationship between regularity and the number of vertices of the graph that makes it possible to build a family of regular graphs, called harmonic graphs. Then, we show that every harmonic graph of degree k can be obtained as successive composition of complete graphs of degree k. We conclude by proving that the harmonic graphs do not have a cut vertex, that implies that every graph of this family has vertex connectivity .
Keywords:
harmonic graphs; graph composition; vertex connectivity