Hopf insulators are characterized by a topological invariant called the Hopf index which classifies maps from three-sphere to two-sphere, instead of a Chern number or a Chern parity. In contrast to a topological insulator, the Hopf insulator is not protected by any kind of symmetry. By dimensional reduction, we argue that there exists a new type of Z(2) index for 2D Hamiltonian with a vanishing...

In this paper, pretopological and topological operators are introduced based on partially continuous linear transformations of the membership and non-membership functions for intuitionistic fuzzy sets. They turn out to be a generalization of the topological operators for intuitionistic fuzzy sets.On the other hand it is a generalization of the fuzzy set pretopological operators introduced...

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

Let G be a simple connected graph with n vertices and m edges and let d(e1) > d(e2) > · · · > d(em) be edge degree sequence of graph G. Denote by EF = ∑m i=1 d(ei) 3 reformulated forgotten index of G. Lower and upper bounds for the invariant EF are obtained.

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. In this paper we introduce four Z 2 topological indices ␨ k =0,1 at k = ͑0,0͒, ͑0,␲͒, ͑␲ ,0͒, and ͑␲ , ␲͒ characterizing 16...

We discuss the Witten index in terms of Krein's spectral shift function, and prove invariance of the Witten index under suitable relative trace class hypotheses.

During the last two decades a large number of numerical graph invariants (topological indices) have been defined and used for correlation analysis in theoretical chemisty, pharmacology, toxicology, and environmental chemistry. However, no systematic study has been undertaken to determine to what extent these indices are correlated with each other. In the present paper we have carried out a prin...

The rst Zagreb index of a graph is equal to the sum of the square of the vertex degrees of the graph and the forgotten topological index (Findex) of a graph is de ned as the sum of cubes of the vertex degrees of the graph. These parameters have applications in chemistry and drug structures. For any xed integer d ≥ 2, the d-ary tree is a rooted tree in which each node has no more than d children...

The intercorrelation between a series of physicochemical parameters and topological indices for a set of beta-blockers is investigated. Partition coefficients are calculated using the ClogP program, and the results are compared with previous data, both experimental and theoretical. These data are complemented by hydrophilicity and solubility calculations, together with the determination of mole...