RETRACTED ARTICLE: A study on harmonious chromatic number of total graph of central graph of generalized Petersen graph

Abstract

For a given graph $$G$$ , $$\chi_{h} \left( G \right)$$ is the least integer of colors such that no two adjacent nodes receive the same color and each combination of color seems together on at most one line. The least number of compartments into which a warehouse should be partitioned to store chemicals certain pairs of which are incompatible is again the chromatic number of the conflict graph. In this article we have found the harmonious coloring of central graph of generalized Petersen graph and have characterized the harmonious chromatic number with the maximum matching number and further we have found the total graph of central graph of generalized Petersen graph using the clique. Clique is a complete graph where every vertex is adjacent to every other. In computational biology we use cliques as a technique of abstracting pair wise relationships consisting of protein–protein interaction or gene similarity. In the latter case we would need to set up a side among the vertices representing two genes if the ones genes have say comparable expression profiles over several time factors of an experiments to study the health care information of patients.