The area of graph theory (GT) is rapidly expanding and playing a significant role in cheminformatics, mostly mathematics chemistry to develop different physicochemical, chemical structure, their properties. manipulation study graphical details are made feasible by using numerical structure invariant. Investigating these characteristics topological indices (TIs) possible the discipline mathemati...

In this paper, we introduce the atom bond connectivity E-Banhatti index and sum of a graph. Also compute these newly defined indices for wheel graphs, friendship chain silicate networks, honeycomb networks nanotubes.

Topological indices are numerical parameters of a graph which characterize its topology. In this paper the PI, Szeged and Zagreb group indices of the tetrameric 1,3–adamantane are computed.

We construct a realization of the algebra of the Z3-graded topological symmetry of type (1, 1, 1) in terms of a pair of operators D1 : H1 → H2, D2 : H2 → H3 satisfying [D1D † 1,D † 2D2] = 0. We show that the sequence of the restriction of these operators to the zero-energy subspace forms a complex and establish the equality of the corresponding topological invariants with the analytic indices o...

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...

An automated PLS engine, WB-PLS, was applied to 1632 QSAR series with at least 25 compounds per series extracted from WOMBAT (WOrld of Molecular BioAcTivity). WB-PLS extracts a single Y variable per series, as well as pre-computed X variables from a table. The table contained 2D descriptors, the drug-like MDL 320 keys as implemented in the Mesa A&C Fingerprint module, and in-house generated top...

In this paper, we extend the recently introduced vertex-degree-based topological index, Sombor and call it general index. The index generalizes both forgotten We present bounds in terms of other important graph parameters for also explore Nordhaus–Gaddum-type result further relations between generalized indices: Randić sum-connectivity