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

scholarly journals Plane Embeddings of Planar Graph Metrics

2007 ◽  
Vol 38 (3) ◽  
pp. 615-637 ◽  
Author(s):  
MohammadHossein Bateni ◽  
Erik D. Demaine ◽  
MohammadTaghi Hajiaghayi ◽  
Mohammad Moharrami
Keyword(s):  
Planar Graph ◽  
Graph Metrics ◽  
Plane Embeddings

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.

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

scholarly journals Measuring Dynamic Changes in the Spatial Pattern and Connectivity of Surface Waters Based on Landscape and Graph Metrics: A Case Study of Henan Province in Central China

Land ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 471
Author(s):  
Bo Mu ◽  
Guohang Tian ◽  
Gengyu Xin ◽  
Miao Hu ◽  
Panpan Yang ◽  
...  
Keyword(s):  
Surface Water ◽  
Nearest Neighbor ◽  
Dynamic Change ◽  
Henan Province ◽  
Central China ◽  
Node Degree ◽  
Human Society ◽  
Stepping Stones ◽  
Dynamic Changes ◽  
Graph Metrics

An understanding of the scientific layout of surface water space is crucial for the sustainable development of human society and the ecological environment. The objective of this study was to use land-use/land-cover data to identify the spatiotemporal dynamic change processes and the influencing factors over the past three decades in Henan Province, central China. Multidisciplinary theories (landscape ecology and graph theory) and methods (GIS spatial analysis and SPSS correlation analysis) were used to quantify the dynamic changes in surface water pattern and connectivity. Our results revealed that the water area decreased significantly during the periods of 1990–2000 and 2010–2018 due to a decrease in tidal flats and linear waters, but increased significantly in 2000–2010 due to an increase in patchy waters. Human construction activities, socioeconomic development and topography were the key factors driving the dynamics of water pattern and connectivity. The use of graph metrics (node degree, betweenness centrality, and delta probability of connectivity) in combination with landscape metrics (Euclidean nearest-neighbor distance) can help establish the parameters of threshold distance between connected habitats, identify hubs and stepping stones, and determine the relatively important water patches that require priority protection or development.

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.

NEIGHBOR SUM DISTINGUISHING COLORING OF SOME GRAPHS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250047 ◽  
Author(s):  
AIJUN DONG ◽  
GUANGHUI WANG
Keyword(s):  
Planar Graph ◽  
Edge Coloring ◽  
Proper Edge Coloring

A proper [k]-edge coloring of a graph G is a proper edge coloring of G using colors of the set [k] = {1, 2,…,k}. A neighbor sum distinguishing [k]-edge coloring of G is a proper [k]-edge coloring of G such that for each edge uv ∈ E(G), the sum of colors taken on the edges incident to u is different from the sum of colors taken on the edges incident to v. By ndiΣ(G), we denote the smallest value k in such a coloring of G. In this paper, we obtain that (1) ndiΣ(G) ≤ max {2Δ(G) + 1, 25} if G is a planar graph, (2) ndiΣ(G) ≤ max {2Δ(G), 19} if G is a graph such that mad(G) ≤ 5.

scholarly journals Asymmetric two-colourings of graphs in S3

2002 ◽  
Vol 132 (2) ◽  
pp. 267-280 ◽  
Author(s):  
ERICA FLAPAN ◽  
DAVID LINNAN LI
Keyword(s):  
Planar Graph

We prove that for any non-planar graph H, we can choose a two-colouring G of H such that G is intrinsically chiral, and if H is 3-connected and is not K3,3 or K5, then G is intrinsically asymmetric. No such asymmetric two-colouring is possible for K3,3 or K5.

Sign in / Sign up

Export Citation Format

Share Document