scholarly journals A Novel Algorithm for Adjacent Vertex-Distinguishing Edge Coloring of Large-scale Random Graphs

2021 ◽  
Vol 14 (3) ◽  
pp. 69-75
Author(s):  
Zhao Huanping ◽  
Zhu Peijin ◽  
Li Jingwen ◽  
Shi Huojie
Keyword(s):  
Random Graphs ◽  
Large Scale ◽  
Edge Coloring ◽  
Adjacent Vertex ◽  
Novel Algorithm

Random graphs

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Large Scale ◽  
Random Network ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Random Graph Model ◽  
Definition Of ◽  
Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

Adjacent vertex distinguishing edge coloring of planar graphs without 3-cycles

2020 ◽  
Vol 12 (04) ◽  
pp. 2050035
Author(s):  
Danjun Huang ◽  
Xiaoxiu Zhang ◽  
Weifan Wang ◽  
Stephen Finbow
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Edge Coloring ◽  
Discrete Math ◽  
Adjacent Vertex ◽  
Chromatic Index ◽  
Proper Edge Coloring ◽  
Minimum Number

The adjacent vertex distinguishing edge coloring of a graph [Formula: see text] is a proper edge coloring of [Formula: see text] such that the color sets of any pair of adjacent vertices are distinct. The minimum number of colors required for an adjacent vertex distinguishing edge coloring of [Formula: see text] is denoted by [Formula: see text]. It is observed that [Formula: see text] when [Formula: see text] contains two adjacent vertices of degree [Formula: see text]. In this paper, we prove that if [Formula: see text] is a planar graph without 3-cycles, then [Formula: see text]. Furthermore, we characterize the adjacent vertex distinguishing chromatic index for planar graphs of [Formula: see text] and without 3-cycles. This improves a result from [D. Huang, Z. Miao and W. Wang, Adjacent vertex distinguishing indices of planar graphs without 3-cycles, Discrete Math. 338 (2015) 139–148] that established [Formula: see text] for planar graphs without 3-cycles.

ALGORITHM OF ε-SVR BASED ON A LARGE-SCALE SAMPLE SET: STEP-BY-STEP SEARCH

2011 ◽  
Vol 09 (02) ◽  
pp. 197-210 ◽  
Author(s):  
SHAOHUA ZENG ◽  
Y. Y. TANG ◽  
YAN WEI ◽  
YONG WANG
Keyword(s):  
Time Complexity ◽  
Large Scale ◽  
Training Sample ◽  
Support Vectors ◽  
Hyper Plane ◽  
Sample Set ◽  
Novel Algorithm

In view of the support vectors of ε-SVR that are not distributed in the ε belt and only located on the outskirts of the ε belt, a novel algorithm to construct ε-SVR of a large-scale training sample set is proposed in this paper. It computes firstly the ε-SVR hyper-plane of a small training sample set and the distances d of all samples to the hyper-plane, then deletes the samples not in field ε ≤ d ≤ d max and searches SVs gradually in the scope ε ≤ d ≤ d max , and trains step-by-step the final ε-SVR. Finally, it analyzes the time complexity of the algorithm, and verifies its convergence in the theory and tests its efficiency by the simulation.

On the Adjacent Vertex Distinguishing Proper Edge Colorings of Several Classes of Complete 5-Partite Graphs

2013 ◽  
Vol 333-335 ◽  
pp. 1452-1455
Author(s):  
Chun Yan Ma ◽  
Xiang En Chen ◽  
Fang Yang ◽  
Bing Yao
Keyword(s):  
Chromatic Number ◽  
Edge Coloring ◽  
Adjacent Vertex ◽  
Chromatic Numbers ◽  
Edge Colorings ◽  
Proper Edge Coloring ◽  
Minimum Number

A proper $k$-edge coloring of a graph $G$ is an assignment of $k$ colors, $1,2,\cdots,k$, to edges of $G$. For a proper edge coloring $f$ of $G$ and any vertex $x$ of $G$, we use $S(x)$ denote the set of thecolors assigned to the edges incident to $x$. If for any two adjacent vertices $u$ and $v$ of $G$, we have $S(u)\neq S(v)$,then $f$ is called the adjacent vertex distinguishing proper edge coloring of $G$ (or AVDPEC of $G$ in brief). The minimum number of colors required in an AVDPEC of $G$ is called the adjacent vertex distinguishing proper edge chromatic number of $G$, denoted by $\chi^{'}_{\mathrm{a}}(G)$. In this paper, adjacent vertex distinguishing proper edge chromatic numbers of several classes of complete 5-partite graphs are obtained.

scholarly journals MR-IDPSO: a novel algorithm for large-scale dynamic service composition

2015 ◽  
Vol 20 (6) ◽  
pp. 602-612 ◽  
Author(s):  
Yanping Zhang ◽  
Zihui Jing ◽  
Yiwen Zhang
Keyword(s):  
Service Composition ◽  
Large Scale ◽  
Dynamic Service Composition ◽  
Novel Algorithm

Upper bounds for adjacent vertex-distinguishing edge coloring

2017 ◽  
Vol 35 (2) ◽  
pp. 454-462 ◽  
Author(s):  
Junlei Zhu ◽  
Yuehua Bu ◽  
Yun Dai
Keyword(s):  
Edge Coloring ◽  
Upper Bounds ◽  
Adjacent Vertex

Novel algorithm of large-scale simultaneous linear equations

2010 ◽  
Vol 22 (7) ◽  
pp. 074206
Author(s):  
T Fujiwara ◽  
T Hoshi ◽  
S Yamamoto ◽  
T Sogabe ◽  
S-L Zhang
Keyword(s):  
Large Scale ◽  
Linear Equations ◽  
Simultaneous Linear Equations ◽  
Novel Algorithm

scholarly journals A Statistical Pipeline for Identifying Physical Features that Differentiate Classes of 3D Shapes

2019 ◽  
Author(s):  
Bruce Wang ◽  
Timothy Sudijono ◽  
Henry Kirveslahti ◽  
Tingran Gao ◽  
Douglas M. Boyer ◽  
...  
Keyword(s):  
Morphological Variation ◽  
Large Scale ◽  
Pairwise Comparisons ◽  
Simulation Framework ◽  
Morphometric Variation ◽  
Global Patterns ◽  
Physical Features ◽  
3D Shapes ◽  
Novel Algorithm

AbstractThe recent curation of large-scale databases with 3D surface scans of shapes has motivated the development of tools that better detect global patterns in morphological variation. Studies which focus on identifying differences between shapes have been limited to simple pairwise comparisons and rely on pre-specified landmarks (that are often known). We present SINATRA: the first statistical pipeline for analyzing collections of shapes without requiring any correspondences. Our novel algorithm takes in two classes of shapes and highlights the physical features that best describe the variation between them. We use a rigorous simulation framework to assess our approach. Lastly, as a case study, we use SINATRA to analyze mandibular molars from four different suborders of primates and demonstrate its ability recover known morphometric variation across phylogenies.

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