Abstract: Functional decomposition is a process of representing a complex function as a function of smaller functions. The size of the decomposed and the number of don't cares it contains is determined during the encoding process. This work proposes a novel input-output encoding approach that minimizes the size of both decomposed function and introduces additional don 't cares in the decomposed functions. The weighted graph approach heuristically determines the optimal encoding. The approach has been implemented and tested using the MCNC benchmarks and the decompose d functions are optimal.