scholarly journals Computing weighted Szeged and PI indices from quotient graphs

2019 ◽  
Vol 119 (21) ◽  
Author(s):  
Niko Tratnik
Keyword(s):  
Quotient Graphs

Topological crystallography of gas hydrates

2015 ◽  
Vol 71 (4) ◽  
pp. 444-450 ◽  
Author(s):  
Sergey V. Gudkovskikh ◽  
Mikhail V. Kirov
Keyword(s):  
Hydrogen Bonding ◽  
Gas Hydrates ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Hexagonal Structure ◽  
New Approach ◽  
Quotient Graphs ◽  
Disordered Structure ◽  
Unit Cells ◽  
Cubic Structure

A new approach to the investigation of the proton-disordered structure of clathrate hydrates is presented. This approach is based on topological crystallography. The quotient graphs were built for the unit cells of the cubic structure I and the hexagonal structure H. This is a very convenient way to represent the topology of a hydrogen-bonding network under periodic boundary conditions. The exact proton configuration statistics for the unit cells of structure I and structure H were obtained using the quotient graphs. In addition, the statistical analysis of the proton transfer along hydrogen-bonded chains was carried out.

Topological features in crystal structures: a quotient graph assisted analysis of underlying nets and their embeddings

2016 ◽  
Vol 72 (3) ◽  
pp. 268-293 ◽  
Author(s):  
Jean-Guillaume Eon
Keyword(s):  
Crystal Structures ◽  
Direct Analysis ◽  
Building Blocks ◽  
Quotient Graph ◽  
Quotient Graphs ◽  
Edge Contraction ◽  
Topological Features ◽  
Structure Decomposition ◽  
Bond Topology ◽  
Ring Analysis

Topological properties of crystal structures may be analysed at different levels, depending on the representation and the topology that has been assigned to the crystal. Considered here is thecombinatorialorbond topologyof the structure, which is independent of its realization in space. Periodic nets representing one-dimensional complexes, or the associated graphs, characterize the skeleton of chemical bonds within the crystal. Since periodic nets can be faithfully represented by their labelled quotient graphs, it may be inferred that their topological features can be recovered by a direct analysis of the labelled quotient graph. Evidence is given for ring analysis and structure decomposition into building units and building networks. An algebraic treatment is developed for ring analysis and thoroughly applied to a description of coesite. Building units can be finite or infinite, corresponding to 1-, 2- or even 3-periodic subnets. The list of infinite units includes linear chains or sheets of corner- or edge-sharing polyhedra. Decomposing periodic nets into their building units relies on graph-theoretical methods classified assurgery techniques. The most relevant operations are edge subdivision, vertex identification, edge contraction and decoration. Instead, these operations can be performed on labelled quotient graphs, evidencing in almost a mechanical way the nature and connection mode of building units in the derived net. Various examples are discussed, ranging from finite building blocks to 3-periodic subnets. Among others, the structures of strontium oxychloride, spinel, lithiophilite and garnet are addressed.

Topological transformations performed on nets via their quotient graphs

2006 ◽  
Vol 221 (1) ◽  
Author(s):  
Jean-Guillaume Eon
Keyword(s):  
Quotient Graph ◽  
Quotient Graphs ◽  
Edge Transitive ◽  
Topological Transformations

AbstractTopological transformations in nets resulting from the insertion or deletion of edges or vertices are analyzed through the analogous operations performed on their quotient graphs. The role of strong rings and cages of the net is emphasized. It is shown that closed trails of the oriented quotient graph define the topology of 3-periodic nets derived from regular, vertex and edge transitive, 4-periodic minimal nets.

scholarly journals On bandwidth, cutwidth, and quotient graphs

1995 ◽  
Vol 29 (6) ◽  
pp. 487-508 ◽  
Author(s):  
Dominique Barth ◽  
François Pellegrini ◽  
André Raspaud ◽  
Jean Roman
Keyword(s):  
Quotient Graphs

Groupoids and labelled quotient graphs: a topological analysis of the modular structure in pyroxenes

2017 ◽  
Vol 73 (3) ◽  
pp. 238-245
Author(s):  
Jean-Guillaume Eon
Keyword(s):  
Topological Analysis ◽  
Modular Structure ◽  
Quotient Graph ◽  
Quotient Graphs ◽  
Partial Symmetry ◽  
Symmetry Operations

The analysis of the modular structure of pyroxenes, recently discussed in Nespolo & Aroyo [Eur. J. Mineral.(2016),28, 189–203], has been performed on the respective labelled quotient graphs (LQGs). It is shown that the structure and maximum symmetry of the module,i.e.its layer group, can be determined directly from the LQG. Partial symmetry operations between different modules have been associated with automorphisms of the quotient graph that may not be consistent with net voltages over the respective cycles. These operations have been shown to generate the pyroxene groupoid structure.

Surface embeddings of the Klein and the Möbius–Kantor graphs

2018 ◽  
Vol 74 (3) ◽  
pp. 223-232
Author(s):  
Martin Cramer Pedersen ◽  
Olaf Delgado-Friedrichs ◽  
Stephen T. Hyde
Keyword(s):  
Two Dimensional ◽  
Hyperbolic Surfaces ◽  
Invariant Representation ◽  
Finite Graphs ◽  
Quotient Graphs ◽  
Arbitrary Genus ◽  
Genus 2

This paper describes an invariant representation for finite graphs embedded on orientable tori of arbitrary genus, with working examples of embeddings of the Möbius–Kantor graph on the torus, the genus-2 bitorus and the genus-3 tritorus, as well as the two-dimensional, 7-valent Klein graph on the tritorus (and its dual: the 3-valent Klein graph). The genus-2 and -3 embeddings describe quotient graphs of 2- and 3-periodic reticulations of hyperbolic surfaces. This invariant is used to identify infinite nets related to the Möbius–Kantor and 7-valent Klein graphs.

scholarly journals CSF/serum quotient graphs for the evaluation of intrathecal C4 synthesis

2009 ◽  
Vol 6 (1) ◽  
pp. 8 ◽  
Author(s):  
Barbara Padilla-Docal ◽  
Alberto J Dorta-Contreras ◽  
Raisa Bu-Coifiu-Fanego ◽  
Alexis Rey
Keyword(s):  
Quotient Graphs
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