G. Polya laid the foundation of counting polynomials in chemical graph theory. These polynomials can be associated with various graphs to signify their properties. In this study, a new concept has been introduced to construct the counting polynomials such as, Sadhana Theta and PI polynomials in terms of omega polynomial. A star expression has been established in order to transform equidistant into non equidistant edges. Furthermore, new relations have also been evolved to calculate Theta, PI and Sadhana Indices through Omega polynomial.