Optimization of Harmonious coloring problem in Uniform theta graph and torus Network

Abstract

Coloring of graphs has been extraordinarily widened areas of investigation. A coloring of a graph can be depicted by a capacity that maps pieces of a graph into some plan of numbers commonly called labels or hues, all together that some property is satisfied. In this article we deal with the harmonious chromatic number of central graph of generalized uniform theta graph and torus network. A coloring c: V → ℕ of the nodes is a harmonious coloring if and only if the coloring is proper and for each and every line (e 1, e 2) ∈ E the line color (c(e 1), c(e 2)) is distinctive that is it emerge solely once.