Yeh and Parhami [6] introduced the concept of the index-permutation graph model, which is an extension of the Cayley graph model and applied it to the systematic development of communication-efficient interconnection networks. Inspiring the concept of building a relationship between an index and a permutation symbol, we make use in this chapter of the spectral null equations variables in each grouping by representing only their corresponding indices in a permutation sequence form. In another way, these indices will be presented by a permutation sequence, where the symbols refer to the position of the corresponding variables in the spectral null equation.