Results 261 to 270 of about 3,892,377 (304)

On reciprocal molecular topological index

Journal of Mathematical Chemistry, 2007
We 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 ...
Bo Zhou, Nenad Trinajstić
exaly   +2 more sources

Generalized Topological Index

K-Theory, 1997
The topological index was defined by Atiyah and Singer [see \textit{M. F. Atiyah} and \textit{I. M. Singer}, ``The index of elliptic operators. I'', Ann. Math., II. Ser. 87, 484-530 (1968; Zbl 0164.24001)] and they showed that this index satisfies three axioms: excision, multiplicativity and normalization.
Foth, Philip A., Tamarkin, Dmitry E.
openaire   +1 more source

Molecular topological index

Journal of Chemical Information and Computer Sciences, 1990
The molecular topological index (MTI) has been systematically tested for counterexamples (two or more nonisomorphic structures with the same MTI number). The analysis was carried out for alkane trees with up to 16 atoms. The search for counterexamples was positive : the first pair of alkane trees with identical MTI numbers was found in the octane ...
Wolfgang R. Mueller, Klaus Szymanski, Jan V. Knop, Nenad Trinajstic   +3 more
openaire   +1 more source

A Novel Quantum-Topology Index

Journal of Chemical Information and Computer Sciences, 2000
By modifying the delta values of molecular connectivity indexes, new quantum-topology descriptors are presented in this paper. Their ability to describe molecular structure, both geometric and electronic, is established by correlating them with the bonding energy (E), force constant (kappa), and radius (R) of a heterogeneous set of monohydrides, as ...
Xinhua Li, Qingsen Yu, Longguan Zhu
openaire   +3 more sources

On the forgotten topological index of graphs

Discrete Mathematics, Algorithms and Applications, 2020
The forgotten topological index of a graph [Formula: see text] is defined as the sum of weights [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] in [Formula: see text], respectively. In this paper,
openaire   +2 more sources

On Hall and Kier's Topological State and Total Topological Index

Journal of Chemical Information and Computer Sciences, 1994
The 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
openaire   +1 more source

A Z2-topological index as a Z2-state index

Journal of Mathematical Physics, 2022
Within 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, L. C. P. A. M. Müssnich, A. F. Reyes-Lega   +2 more
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An index of topological preservation for feature extraction

Pattern Recognition, 1995
Abstract This paper is about the ability of principal components analysis, the Sammon algorithm, and an extension of the Kohonen self-organizing feature map to preserve spatial order during feature extraction on unlabeled data. Transformations to q -space that preserve the order of all pairwise distances in any set of vectors in p -space are ...
James C. Bezdek, Nikhil R. Pal
openaire   +2 more sources

On Highly Discriminating Molecular Topological Index

Journal of Chemical Information and Computer Sciences, 1996
A highly discriminating molecular topological index, EAID, is proposed based on the extended adjacency matrix. A systematic search for degeneracy was performed for 3 807 434 alkane trees, 202 558 complex cyclic or polycyclic graphs, and 430 472 structures containing heteroatoms.
Chang-Yu Hu, Lu Xu
openaire   +1 more source

On the forgotten topological index

2017
Summary: 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.
openaire   +1 more source