The representation of chemical compounds and chemical networks with the M-polynomials is a new idea and it gives nice and good results of the topological indices. These results are used to correlate the chemical compounds and chemical networks with their chemical properties and bioactivities. Particular attention is paid to the derivation of the M polynomia- for the benzene ring embedded in the P-type surface network in 2D. Furthermore, the topological indices based on the degrees are also derived by using the general form of M-polynomial of benzene ring embedded in the P-type surface network BR(m, n). In the end, the graphical representation and comparison of the M-polynomial and the topological indices of benzene ring embedded in P-type surface network in 2D are described.