One possibility for the formulation of the RWA problem in transparent networks is the creation of an auxiliary undirected graph with vertices representing lightpaths in the network. Coloring graphs is an NP-Hard problem and various heuristics have been proposed for the solution of wavelength assignment problem in optical networks. This letter introduces an approach for exact solution for the assignment of wavelengths to lightpaths in transparent networks using a novel Parameterized Complexity Theory.127523525