Topolojik indekslerin matematiksel kimyada kulanım alanı bulunmaktadır. Uzaklık-bazlı topolojik ise moleküler graf teoride oldukça önemi vardır. Harary indeksi uzaklık-bazlı bir değişmezidir. Yakın zamanda cebirsel yapı üzerinde nokta çarpım grafı çalışıldı. Bu çalışmada da bu grafın verilecektir.

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, we determined the extremal (maximal and minimal) unicyclic and bicyclic graphs with respect to Harary index. 2010 Mathematics Subject Classification: 05C90

Introduced in 1947, the Wiener index W (T ) = ∑ {u,v}⊆V (T ) d(u, v) is one of the most thoroughly studied chemical indices. The extremal structures (in particular, trees with various constraints) that maximize or minimize the Wiener index have been extensively investigated. The Harary index H(T ) = ∑ {u,v}⊆V (T ) 1 d(u,v) , introduced in 1993, can be considered as the “reciprocal analogue” of ...

recently, hua et al. defined a new topological index based on degrees and inverse ofdistances between all pairs of vertices. they named this new graph invariant as reciprocaldegree distance as 1{ , } ( ) ( ( ) ( ))[ ( , )]rdd(g) = u v v g d u  d v d u v , where the d(u,v) denotesthe distance between vertices u and v. in this paper, we compute this topological index forgrassmann graphs.

One of considerable topics in chemistry is surveying the quantitative structure-property relationship between the structure of a molecule and chemical, physical and biological properties of it(QSPR). For this purpose, the form of molecule must be coded according to numbers. A common method, for coding the molecule structure, is to assign a graph to the molecule, where the vertices are atoms of ...

The Harary index H can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms, such that their magnitude decreases with the increasing distance between the respective two atoms. A generalization of the Harary index, denoted by Hk, is achieved by employing the Steiner-type distance between k-tuples of atoms. We show that the linear c...