M-Polynomials and Degree-Based Topological Indices of Mycielskian of Paths and Cycles

For a graph G, the M-polynomial is defined as M(G;x, y) = sigma delta <=alpha <=beta <= increment m alpha beta(G)x alpha y beta, where m alpha beta(alpha,beta >= 1), is the number of edges ab of G such that degG(a) = alpha and degG(b) = beta, and delta is the minimum degree and increment is the maximum degree of G. The physiochemical properties of chemical graphs are found by topological indices, in particular, the degree-based topological indices, which can be determined from an algebraic formula called M-polynomial. We compute the closest forms of M-polynomial for Mycielskian of paths and cycles. Further, we plot the 3-D graphical representation of M-polynomial. Finally, we derive some degree-based topological indices with the help of M-polynomial.