We show that the special case of Serre duality involved in the Borel-Bott-Weil theorem can be formulated and proved in the context of equi-variant Kasparov theory by combining the Atiyah-Singer index theorem and the framework of equivariant correspondences developed in another paper by the first author and Ralf Meyer. The twisted Dolbeault cohomology groups of a flag variety that figure in the ...

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors, one of the earliest and most widely used being the Wiener index W, derived from the interatomic distances in a molecular graph. Extensive use of such structural descriptors or topological indices has been made in drug design, screening of chemical databases, and similarity and diversit...

It is well known that the chemical behavior of a compound is dependent upon the structure of itsmolecules. Quantitative structure – activity relationship (QSAR) studies and quantitative structure –property relationship (QSPR) studies are active areas of chemical research that focus on the nature ofthis dependency. Topological indices are the numerical value associated with chemical constitution...

Three new distance—based topological indices are described; two of them, D and D1 (mean distance topological indices, for any graphs, and for acyclic graphs, respectively) have a modest discriminating ability but may be useful for correlations, e. g. with octane numbers. The third index, J (average distance sum connectivity) is the least degenerate single topological index proposed till now. Th...

In quantitative structure-property and structure-activity relationships studies, several graph invariants, namely, topological indices have been defined studied due to their numerous applications in computer networks, biotechnology, nanochemistry. Topological are numeric parameters that describe the biological, physical, chemical properties depending on structure topology of different compounds...

The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete k-partite graph whose partition...

Topological Chern indices are related to the number of rotational states in each molecular vibrational band. Modification of the indices is associated to the appearance of "band degeneracies," and exchange of rotational states between two consecutive bands. The topological dynamical origin of these indices is demonstrated through a semiclassical approach, and their values are computed in two ex...

Graph theory has provided a very useful tool, called topological indices which are a number obtained from the graph $G$ with the property that every graph $H$ isomorphic to $G$, value of a topological index must be same for both $G$ and $H$. In this article, we present exact expressions for some topological indices of k-th subdivision graph and semi total point graphs respectively, which are a ...