Number of wavelengths required in m-arity tree networks

A theory to allocate a wavelength in the tree networks coordinated arrangement in m-arity networks is proposed. Wavelength required equations to support all-to-all unicasting in the network according to its depth are presented. Three cases are examined: when nodes are only targets, sources or target and source in the same time. The trade-off between wavelength cost and wavelength conversion cost is considered; therefore, concentration is on wavelength allocation without conversion.