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...

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...

Yoshiaki NAKAZAWA*, Kenji TAMURA *, Michitaka YOSHIDA* Katsutoshi TAKAGI† and Mitsutoshi KANO† * Sumitomo Metal Industries, Ltd. Corporate Research and Development Laboratories 1-8 Fuso-cho, Amagasaki, Hypgo, 660-0891, Japan e-mail: [email protected], web page: http://www. sumitomometals.co.jp †Toyoda Iron Works CO., LTD. Product Research and Development DIV.NO.2 4-50 Hosoya-cho...

For a connected graph G and an non-empty set S ⊆ V (G), the Steiner distance dG(S) among the vertices of S is defined as the minimum size among all connected subgraphs whose vertex sets contain S. This concept represents a natural generalization of the concept of classical graph distance. Recently, the Steiner Wiener index of a graph was introduced by replacing the classical graph distance used...

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...