It is proved that any molecular graph invariant (that is any topological index) can be uniquely represented as (1) a linear combination of occurrence numbers of some substructures (fragments), both connected and disconnected, or (2) a polynomial on occurrence numbers of connected substructures of corresponding molecular graph. Besides, any (0,l)-valued molecular graph invariant can be uniquely ...

<abstract><p>In this work we obtain new lower and upper optimal bounds of general Sombor indices. Specifically, get inequalities for these indices relating them with other indices: the first Zagreb index, forgotten index variable index. Finally, solve some extremal problems indices.</p></abstract>

The topological index of a surface was previously introduced by the first author as the topological analogue of the index of an unstable minimal surface. Here we show that surfaces of arbitrarily high topological index exist. Consider a compact, connected, two sided surface S properly embedded in a compact, orientable 3-manifold M . The disk complex Γ(S) is the simplicial complex defined as fol...

Spirituality........A single word yet with many definitions due to the fact that it may comprise several aspects of human existence. Spirituality is often linked to the human spirit thus it is considered as a superior component for human existence [1]. Furthermore, it is recognized as one of the basic components of health and well-being and as a basic dimension of wellness along with others suc...

Polynomial interpolation can be used to obtain closed formulas for topological indices of infinite series of molecular graphs. The method is discussed and its advantages and limitations are pointed out. This is illustrated on fullerenes C12k+4 and four topological indices: the Wiener index, the edge Wiener index, the eccentric connectivity index, and the reverse Wiener index. The results for th...

The molecular structures are modelled as graphs which called the graphs. In these graphs, each vertex represents an atom and edge denotes covalent bond between atoms. It is shown that topological indices defined on can reflect chemical characteristics of compounds drugs. A large number previous drug experiments revealed there strong inherent connections drug’s bio-medical pharmacology character...

We study twisted Spin-manifolds over a paracompact Hausdorff space X with a twisting α : X → K(Z, 3). We introduce the topological index and the analytical index on the bordism group of α-twisted Spin-manifolds over (X,α), taking values in topological twisted K-homology and analytical twisted K-homology respectively. The main result of this paper is to establish the equality between the topolog...

let g be a connected simple (molecular) graph. the distance d(u, v) between two vertices u and v of g is equal to the length of a shortest path that connects u and v. in this paper we compute some distance based topological indices of h-phenylenic nanotorus. at first we obtain an exactformula for the wiener index. as application we calculate the schultz index and modified schultz index of this ...

A topological index of a graph is a numeric quantity related to a structure of a molecule which is invariant under graph automorphism. Recently, Ghorbani and Hosseinzadeh introduced Fourth Zagreb index of graphs. In this paper we determine a closed formula of this new topological index of the famous Benzenoid family named Circumcoronene series of Benzenoid Hk.

A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate th...