M-Polynomials and Degree-Based Topological Indices of Mycielskian of Paths and Cycles - Shilpa, H. C.; Gayathri, K.; Nagesh, H. M.; Narahari, N. (Communications in Mathematics and Applications, 2023)
For a graph $G$, the M-polynomial is defined as \(M(G;x,y)= \sum_{δ ≤ α ≤ β ≤ Δ}m_{α β}(G)x^{α}y^{β}\), where \(m_{α β} (α, β ≥ 1)\), is the number of edges \(ab\) of \(G\) such that \(\deg_{G}(a)=α\) and \(\deg_{G}(b)=β\), and \(δ\) is the minimum degree and \(Δ\) 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.