M-Polynomial and Degree-Based Topological Indices

2014/07/07 by Deutsch, Emeric, Klavžar, Sandi · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.1592

Abstract

Let G be a graph and let m_ij(G), i,j≥ 1, be the number of edges uv of G such that \d_v(G), d_u(G)\ = \i,j\. The \em M-polynomial of G is introduced with M(G;x,y) = ∑_{i≤ j} m_ij(G)xⁱy^j. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the M-polynomial. The new approach is also illustrated with examples.

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