scholarly journals A TOPOLOGICAL VARIATION OF THE RECONSTRUCTION CONJECTURE

2016 ◽  
Vol 59 (1) ◽  
pp. 221-235
Author(s):  
MAX F. PITZ ◽  
ROLF SUABEDISSEN
Keyword(s):  
Graph Theory ◽  
Cantor Set ◽  
Topological Properties

AbstractThis paper investigates topological reconstruction, related to the reconstruction conjecture in graph theory. We ask whether the homeomorphism types of subspaces of a space X which are obtained by deleting singletons determine X uniquely up to homeomorphism. If the question can be answered affirmatively, such a space is called reconstructible. We prove that in various cases topological properties can be reconstructed. As main result we find that familiar spaces such as the reals ℝ, the rationals ℚ and the irrationals ℙ are reconstructible, as well as spaces occurring as Stone–Čech compactifications. Moreover, some non-reconstructible spaces are discovered, amongst them the Cantor set C.

Graph Theory

2020 ◽  
pp. 354-370
Author(s):  
Seethalakshmi R.
Keyword(s):  
Graph Theory ◽  
Market Structure ◽  
Financial Market ◽  
Network Theory ◽  
Financial Analysts ◽  
Structural Models ◽  
Topological Properties ◽  
Strategic Decisions ◽  
Analytical Geometry ◽  
Innovative Methods

Mathematics acts an important and essential need in different fields. One of the significant roles in mathematics is played by graph theory that is used in structural models and innovative methods, models in various disciplines for better strategic decisions. In mathematics, graph theory is the study through graphs by which the structural relationship studied with a pair wise relationship between different objects. The different types of network theory or models or model of the network are called graphs. These graphs do not form a part of analytical geometry, but they are called graph theory, which is points connected by lines. The various concepts of graph theory have varied applications in diverse fields. The chapter will deal with graph theory and its application in various financial market decisions. The topological properties of the network of stocks will provide a deeper understanding and a good conclusion to the market structure and connectivity. The chapter is very useful for academicians, market researchers, financial analysts, and economists.

scholarly journals Harmonic measure of the planar Cantor set from the viewpoint of graph theory

1992 ◽  
Vol 109 (1-3) ◽  
pp. 193-202
Author(s):  
Massimo A. Picardello ◽  
Mitchell H. Taibleson ◽  
Wolfgang Woess
Keyword(s):  
Graph Theory ◽  
Harmonic Measure ◽  
Cantor Set

Computation of certain topological properties of para-line graph of honeycomb networks and graphene

2017 ◽  
Vol 09 (05) ◽  
pp. 1750064 ◽  
Author(s):  
Ali Ahmad
Keyword(s):  
Graph Theory ◽  
Topological Index ◽  
Line Graph ◽  
Topological Indices ◽  
Atomic Scale ◽  
Index Formula ◽  
Honeycomb Lattice ◽  
Topological Properties

Graphene is an atomic scale honeycomb lattice made of the carbon atoms. Graph theory has given scientific expert an assortment of helpful apparatuses, for example, topological indices. A topological index [Formula: see text] of a graph [Formula: see text] is a number with the property that for each graph [Formula: see text] isomorphic to [Formula: see text] [Formula: see text] In this paper, we exhibit correct expressions for some topological indices for para-line graph of honeycomb networks and graphene.

scholarly journals On Some Ve-Degree and Harmonic Molecular Topological Properties of Carborundum

2020 ◽  
Vol 8 (1) ◽  
pp. 65
Author(s):  
Murat Cancan ◽  
Kerem Yamaç ◽  
Ziyattin Taş ◽  
Mehmet Şerif Aldemir
Keyword(s):  
Silicon Carbide ◽  
Graph Theory ◽  
Topological Indices ◽  
Topological Properties ◽  
Degree Sum ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Degree Harmonic ◽  
Atom Bond

Carborundum, also known as silicon carbide which containing carbon and silicon, is a semiconductor. Molecular topological properties of physical substances are important tools to investigate the underlying topology of these substances. Ev-degree and ve-degree based on the molecular topological indices have been defined as parallel to their corresponding classical degree based topological indices in chemical graph theory. Classical degree based topological properties of carborundum have been investigated recently. As a continuation of these studies, in this study, we compute novel ve-degree harmonic, ve-degree sum-connectivity, ve-degree geometric-arithmetic, and ve-degree atom-bond connectivity, the first and the fifth harmonic molecular topological indices of two carborundum structures. 

Some topological indices of dendrimers

2020 ◽  
pp. 2050018
Author(s):  
S. Alyar ◽  
R. Khoeilar ◽  
A. Jahanbani
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Topological Indices ◽  
Molecular Structures ◽  
Topological Properties ◽  
Zagreb Index ◽  
Zinc Porphyrin ◽  
Molecular Graphs

There are immense applications of graph theory in chemistry and in the study of molecular structures, and after that, it has been increasing exponentially. Molecular graphs have points (vertices) representing atoms and lines (edges) that represent bonds between atoms. In this paper, we study the molecular graph of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers and analyzed its topological properties. For this purpose, we have computed topological indices, namely the Albertson index, the sigma index, the Nano-Zagreb index, the first and second hyper [Formula: see text]-indices of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers.

scholarly journals On Molecular Topological Properties of TiO2 Nanotubes

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Nilanjan De
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Strong Correlation ◽  
Tio2 Nanotubes ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Topological Properties ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Titania Nanotube

Titania nanotube is a well-known semiconductor and has numerous technological applications. In chemical graph theory, topological indices provide an important tool to quantify the molecular structure and it is found that there is a strong correlation between the properties of chemical compounds and their molecular structure. Among different topological indices, degree-based topological indices are most studied and have some important applications. In this study, several old and new degree-based topological indices have been investigated for titania TiO2 nanotubes.

scholarly journals On molecular topological properties of dendrimers

2016 ◽  
Vol 94 (2) ◽  
pp. 120-125 ◽  
Author(s):  
Syed Ahtsham Ul Haq Bokhary ◽  
Muhammad Imran ◽  
Sadia Manzoor
Keyword(s):  
Graph Theory ◽  
Physicochemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Topological Properties ◽  
Graph Invariant ◽  
Qspr Study ◽  
Atom Bond

Topological indices are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as the Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) indices are used to predict the bioactivity of different chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study the degree-based molecular topological indices such as ABC4 and GA5 for certain families of dendrimers. We derive the analytical closed formulae for these classes of dendrimers.

scholarly journals On Ev-Degree and Ve-Degree Topological Properties of Tickysim Spiking Neural Network

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Murat Cancan
Keyword(s):  
Neural Network ◽  
Graph Theory ◽  
Real Time ◽  
Network Architecture ◽  
Interconnection Network ◽  
Topological Indices ◽  
Spiking Neural Network ◽  
Topological Properties ◽  
Neural Network Architecture

Topological indices are indispensable tools for analyzing networks to understand the underlying topology of these networks. Spiking neural network architecture (SpiNNaker or TSNN) is a million-core calculating engine which aims at simulating the behavior of aggregates of up to a billion neurons in real time. Tickysim is a timing-based simulator of the interchip interconnection network of the SpiNNaker architecture. Tickysim spiking neural network is considered to be highly symmetrical network classes. Classical degree-based topological properties of Tickysim spiking neural network have been recently determined. Ev-degree and ve-degree concepts are two novel degrees recently defined in graph theory. Ev-degree and ve-degree topological indices have been defined as parallel to their corresponding counterparts. In this study, we investigate the ev-degree and ve-degree topological properties of Tickysim spiking neural network. These calculations give the information about the underlying topology of Tickysim spiking neural network.

Altered topological properties of brain networks in the early MS patients revealed by cognitive task-related fMRI and graph theory

2018 ◽  
Vol 40 ◽  
pp. 385-395 ◽  
Author(s):  
Seyedeh Naghmeh Miri Ashtiani ◽  
Mohammad Reza Daliri ◽  
Hamid Behnam ◽  
Gholam-Ali Hossein-Zadeh ◽  
Masoud Mehrpour ◽  
...  
Keyword(s):  
Graph Theory ◽  
Cognitive Task ◽  
Brain Networks ◽  
Topological Properties

scholarly journals Auditory Verbal Hallucination-Specific Functional Brain Networks in Schizophrenia: A Study Based on Graph Theory

2021 ◽  
Author(s):  
Weiliang Yang ◽  
Yan li ◽  
Haiyan Cao ◽  
Wen Qin ◽  
Yongying Cheng ◽  
...  
Keyword(s):  
Graph Theory ◽  
Clinical Features ◽  
Brain Networks ◽  
Brain Network ◽  
Local Network ◽  
Topological Properties ◽  
Network Efficiency ◽  
Functional Brain ◽  
Auditory Verbal Hallucinations ◽  
Functional Brain Networks

Abstract Background Although mounting previous studies have characterized auditory verbal hallucinations (AVH) related brain network abnormalities in the patients with schizophrenia, AVH related brain network alterations based on graph theory was rarely reported. In addition, the relationship between the features of AVH related brain networks based on graph theory and clinical features of schizophrenia patients with AVH is unclear. Our study to explore associations among network metrics, and clinical features in schizophrenia patients with AVH. Method Thirty-one schizophrenia patients without AVH, 17 patients with AVH, and 31 healthy controls were examined by functional magnetic resonance imaging. Graph theory method was performed to analyze the topological properties of functional network in three groups. Results Our results showed that schizophrenia patients with AVH displayed decreased local network efficiency, clustering coefficients, and nodal efficiency of the right dorsolateral prefrontal cortex. Local network efficiency was positively correlated with AVH characteristics. Conclusion The topological properties of brain functional networks are disrupted in schizophrenia patients with AVH, suggesting a role of functional brain networks in the pathogenesis of AVH.

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