scholarly journals Spatial Graph as Connected Sum of a Planar Graph and a Braid

2021 ◽  
Author(s):  
Valeriy G. Bardakov ◽  
Akio Kawauchi
Keyword(s):  
Planar Graph ◽  
Connected Sum ◽  
Spatial Graph

scholarly journals KNOT-INEVITABLE PROJECTIONS OF PLANAR GRAPHS

1996 ◽  
Vol 05 (06) ◽  
pp. 877-883 ◽  
Author(s):  
KOUKI TANIYAMA ◽  
TATSUYA TSUKAMOTO
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Spatial Graph ◽  
Torus Knot ◽  
Nonplanar Graph

For each odd number n, we describe a regular projection of a planar graph such that every spatial graph obtained by giving it over/under information of crossing points contains a (2, n)-torus knot. We also show that for any spatial graph H, there is a regular projection of a (possibly nonplanar) graph such that every spatial graph obtained from it contains a subgraph that is ambient isotopic to H.

THE QUANTUM 𝔰𝔩(3) INVARIANTS OF CUBIC BIPARTITE PLANAR GRAPHS

2008 ◽  
Vol 17 (03) ◽  
pp. 361-375 ◽  
Author(s):  
DONGSEOK KIM ◽  
JAEUN LEE
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Connected Sum

Temperley–Lieb algebras have been generalized to 𝔰𝔩(3,ℂ) web spaces. Since a cubic bipartite planar graph with suitable directions on edges is a web, the quantum 𝔰𝔩(3) invariants naturally extend to all cubic bipartite planar graphs. First we completely classify them as a connected sum of prime webs. We provide a method to find all prime webs. Using the quantum 𝔰𝔩(3) invariants, we provide a criterion which determines the symmetry of cubic bipartite planar graphs. We also provide an example that our criterions for graphs is different from that of links.

Computational Micrograph Registration with Sieve Processes

1996 ◽  
Vol 54 ◽  
pp. 440-441
Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Spatial Organization ◽  
Spatial Arrangement ◽  
Stereo Image ◽  
Image Model ◽  
Geometric Invariants ◽  
Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

Approach to spatial modeling of networks and groups of objects on the basis of the weighted graph construction procedure

2020 ◽  
Vol 964 (10) ◽  
pp. 49-58
Author(s):  
V.I. Bilan ◽  
A.N. Grigor’ev ◽  
G.G. Dmitrikov ◽  
E.A. Dudin
Keyword(s):  
Spatial Configuration ◽  
Weighted Graph ◽  
Edge Length ◽  
Buffer Zones ◽  
Typical Structure ◽  
Spatial Graph ◽  
Object Based ◽  
Complementary Graph ◽  
Spatial Parameters ◽  
The Given

The direction of research on the development of a scientific and methodological tool for the analysis of spatial objects in order to determine their generalized spatial parameters was selected. An approach to the problem of modeling networks and groups of objects based on the synthesis of a weighted graph is proposed. The spatial configuration of objects based on the given conditions is described by a weighted graph, the edge length of which is considered as the weight of the edges. A generalization to the typical structure of a spatial graph is formulated; its essence is representation of nodal elements as two-dimensional (polygonal) objects. To take into account the restrictions on the convergence of the vertices described by the buffer zones, a complementary graph is formed. An algorithm for constructing the implementation of a spatial object based on the sequential determination of vertices that comply with the given conditions is proposed. Using the software implementation of the developed algorithm, an experiment was performed to evaluate the spatial parameters of the simulated objects described by typical graph structures. The following parameters were investigated as spatial ones

scholarly journals A Thomassen-type method for planar graph recoloring

2021 ◽  
Vol 95 ◽  
pp. 103319
Author(s):  
Zdeněk Dvořák ◽  
Carl Feghali
Keyword(s):  
Planar Graph ◽  
Type Method

Plane embeddings of planar graph metrics

2006 ◽  
Author(s):  
MohammadHossein Bateni ◽  
MohammadTaghi Hajiaghayi ◽  
Erik D. Demaine ◽  
Mohammad Moharrami
Keyword(s):  
Planar Graph ◽  
Graph Metrics ◽  
Plane Embeddings

The random division of faces in a planar graph

1996 ◽  
Vol 28 (2) ◽  
pp. 331-331
Author(s):  
Richard Cowan ◽  
Simone Chen
Keyword(s):  
Planar Graph ◽  
Limiting Distribution ◽  
Face Type ◽  
Connected Planar Graph ◽  
Random Division

Consider a connected planar graph. A bounded face is said to be of type k, or is called a k-face, if the boundary of that face contains k edges. Under various natural rules for randomly dividing bounded faces by the addition of new edges, we investigate the limiting distribution of face type as the number of divisions increases.

scholarly journals Effective Action from M-Theory on Twisted Connected Sum G 2-Manifolds

2017 ◽  
Vol 359 (2) ◽  
pp. 535-601 ◽  
Author(s):  
Thaisa C. da C. Guio ◽  
Hans Jockers ◽  
Albrecht Klemm ◽  
Hung-Yu Yeh
Keyword(s):  
Effective Action ◽  
Connected Sum ◽  
M Theory
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