Let G be a graph and let mij(G), i, j ≥ 1, be the number of edges uv of G such that {dv(G), du(G)} = {i, j}. TheM -polynomial ofG is introduced withM(G;x, y) = ∑ i≤j mij(G)x y . 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 -polyn...

Pairwise orthogonal topological indices A and Woo derived from the characteristic graphs of alternant polycyclic aromatic hydrocarbons (kata-annellated and peri-condensed systems) correlate with resonance energy per electron, energy of the HOMO and total ;i: electron energy respectively. For topological indices a high discrimination power is necessary but not sufficient to correlate with molecu...

Topological quantum numbers account for the precise quantization that occurs in the integer Hall effect. In this theory, Kubo’s formula for the conductance acquires a topological interpretation in terms of Chern numbers and their non-commutative analog, the Fredholm Indices.

This paper addresses the problem of incorporating topological indices as structural descriptors for correlating properties in the design of product molecules with fine-tuned or optimized property values. Three different types of topological indices are considered: Randir's molecular connectivity indices, Kier's shape indices and the Wiener Index. The adjacency matrix representation which provid...