Abstract. The energy of a molecular graph is a popular parameter that is defined as the sum of the absolute values of a graph’s eigenvalues. It is well known that the energy is related to the matching polynomial and thus also to the Hosoya index via a certain Coulson integral. Trees minimizing the energy under various additional conditions have been determined in the past, e.g., trees with a gi...

Topological indices are mathematical descriptors for molecular structures. These used to describe physico-chemical properties such as solubility, shape and weight. In this paper, we present distance-based topological Wiener index hyper-Wiener by using Hosoya polynomial inverse graphs associated with finite cyclic group. Also, have found eccentricity based of

In the language of mathematical chemistry, Fibonacci cubes can be defined as the resonance graphs of fibonacenes. Lucas cubes form a symmetrization of Fibonacci cubes and appear as resonance graphs of cyclic polyphenantrenes. In this paper it is proved that the Wiener index of Fibonacci cubes can be written as the sum of products of four Fibonacci numbers which in turn yields a closed formula f...

Novel naphthylenic tori, generated by suitable modifications (that include the leapfrog procedure) of a square net embedded on the torus, are characterised by the ring spiral code, Hosoya polynomial and spectral data. The polynomial is formulated for two series of naphthylenic tori. The Wiener number is calculated by recursive formulae from the first derivative of the Hosoya polynomial, under x...

Weighted Hosoya polynomials have been developed by Diudea, in ref. Studia Univ. "Babes-Bolyai", 2002, 47, 131-139. Among various weighting schemes, those polynomials obtained by using Diudea's Shell matrix operator are far more interesting. We present here the Shell-Distance and Shell-Degree-Distance polynomials and close formulas to calculate them and derived Cluj-Tehran CT index in the family...