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 graph, and let $D[G]$ denote the double graph of $G$. In this paper, we first derive closed-form formulas for different distance based topological indices for $D[G]$ in terms of that of $G$. Finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topologica...

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.

Quantifying the success of the topographic preservation achieved with a neural map is difficult. In this paper we present Topological Correlation, Tc, a method that assesses the degree of topographic preservation achieved based on the linear correlation between the topological distances in the neural map, and the topological distances in the induced Delaunay triangulation of the network nodes. ...

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...

A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.

The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

The expensive and time-consuming process of drug lead discovery is significantly accelerated by efficiently screening molecular libraries with a high structural diversity and selecting subsets of molecules according to their similarity toward specific collections of active compounds. To characterize the molecular similarity/diversity or to quantify the drug-like character of compounds the proce...

the glass transition temperature of several pvac(1)-b-poly(ma-co-mma) (2) terpolymers with different fractions of methyl acrylate (ma) and methyl methacrylate (mma) repeating units in random copolymer (block 2) were calculated with barton, kwei and topological equations. the calculation was on the basis of the correlation between the fraction of repeating units in random copolymers and theoreti...