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A Z2-topological index as a Z2-state index
Journal of Mathematical Physics, 2022Within the setting of infinite-dimensional self-dual CAR C* algebras describing fermions in the Zd lattice, we depart from the well-known Araki–Evans σ(P1,P2)Z2 index for quasi-free fermion states and rewrite it in terms of states rather than in terms of basis projections.
N. J. B. Aza +2 more
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On reciprocal molecular topological index
Journal of Mathematical Chemistry, 2007We report some properties of the reciprocal molecular topological index RMTI of a connected graph, and, in particular, its relationship with the first Zagreb index M-1. We also derive the upper bounds for RMTI in terms of the number of vertices and the number of edges for various classes of graphs, including Kr+1 -free graphs with r >= 2, quadrangle ...
Zhou, Bo, Trinajstić, Nenad
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Topological symmetry identification of kinematic chains based on topological index
Mechanism and Machine Theory, 2020Abstract To improve the synthesis efficiency of kinematic chains (KCs) and mechanisms, the topological symmetry of a chain should be considered. However, the symmetry recognition of pairs is rarely mentioned. Therefore, an index, called the extended adjacency identification index for the symmetry of KCs (SKC-EAID), is proposed to identify the ...
Tao Deng +4 more
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Extension of a Highly Discriminating Topological Index
Journal of Chemical Information and Modeling, 2015A highly discriminating topological index, EAID, is generated in our laboratory. A systematic search for degeneracy was performed on a total of over 14 million structures, and no duplicate occurred. These structures are as follows: over 3.8 million alkane trees with 1-22 carbon atoms; over 0.38 million structures containing heteroatoms; over 4 million ...
Qingyou, Zhang +5 more
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On Hall and Kier's Topological State and Total Topological Index
Journal of Chemical Information and Computer Sciences, 1994The topological state and the total topological index, tau, have been tested systematically. Counterexamples are provided proving that the topological state method cannot determine classes of symmetrically equivalent atoms in a molecule fully correct ...
Chang-Yu Hu, Lu Xu
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On the forgotten topological index
2017Summary: The forgotten topological index of a graph \(G\) is defined as \(F(G)=\sum_{u\in V(G)}d(u)^3\). In this paper, we compute some properties of forgotten index and then, we determine it for some classes of product graphs.
Ghorbani, M., Khaksari, A.
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Forgotten reduced neighborhood topological index
Asian-European Journal of MathematicsTopological graph indices are the most important applications of graph theory. In the last few decades, such applications have been increasingly in use for mathematicians, chemists, pharmacologists. Due to these applications, a large number of these indices are defined and used in several areas.
Anwar Saleh +2 more
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“Topologically Indexed Function Spaces and Adjoint Functors”
Canadian Mathematical Bulletin, 1982AbstractLet Top denote the category of topological spaces and continuous maps. In this paper we discuss families of function spaces indexed by the elements of a topological space T, and their relationship to the characterization of right adjoints Top/S → Top/T, where S is also a topological space. After reducing the problem to the case where S is a one-
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Topological Index and Analytical Index: Reformulation of Index Theory
2019In this part we present the main algebraic structures on topological manifolds and we reformulate the index theory.
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Index Theorems and Noncommutative Topology
2008These lecture notes are mainly devoted to a K-theory proof of the Atiyah-Singer index theorem. Some applications of the K-theory to noncommutative topology are also given.
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