We formulate and prove the special case of Serre duality involved in the Borel-Bott-Weil theorem in the language of equivariant Kasparov theory. The method is to combine 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 the flag variety figuring in the Borel-B...

Topological indices are the mathematical tools that correlate the chemical structure with various physical properties, chemical reactivity or biological activity numerically. A topological index is a function having a set of graphs as its domain and a set of real numbers as its range. In QSAR/QSPR study, a prediction about the bioactivity of chemical compounds is made on the basis of physico-ch...

The connection of Zagreb polynomials and indices to chemical graph theory is a bifurcation mathematical chemistry, which has had crucial influence on the development sciences. Nowadays, study topological become vast effective research area in theory. In this article, we add up eight different for Silicate Network Chain Network. From these polynomials, catch degree-based indices. We also provide...

The Sombor indices, a new category of degree-based topological molecular descriptors, have been widely investigated due to their excellent chemical applicability. This paper aims establish index distributions in random polygonal chain networks and derive expressions for expected values variances. variances the indices polyonino, pentachain, polyphenyl, cyclooctane chains are obtained. Since end...

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...