Coprime Irregular Edge-weighting of Mongolian Tent and Polar Grid graphs

2020 ◽  
Vol 14 (11) ◽  
Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 38 ◽  
Author(s):  
Salama Nagy Daoud

Edge Even Graceful Labelingwas first defined byElsonbaty and Daoud in 2017. An edge even graceful labeling of a simple graph G with p vertices and q edges is a bijection f from the edges of the graph to the set { 2 , 4 , … , 2 q } such that, when each vertex is assigned the sum of all edges incident to it mod 2 r where r = max { p , q } , the resulting vertex labels are distinct. In this paper we proved necessary and sufficient conditions for the polar grid graph to be edge even graceful graph.


2012 ◽  
Vol 34 (5) ◽  
pp. 918-929 ◽  
Author(s):  
A. Gijsenij ◽  
T. Gevers ◽  
J. van de Weijer

2021 ◽  
Vol 37 (3) ◽  
pp. 907-917
Author(s):  
Martin Kreh ◽  
Jan-Hendrik de Wiljes

AbstractIn 2011, Beeler and Hoilman generalized the game of peg solitaire to arbitrary connected graphs. In the same article, the authors proved some results on the solvability of Cartesian products, given solvable or distance 2-solvable graphs. We extend these results to Cartesian products of certain unsolvable graphs. In particular, we prove that ladders and grid graphs are solvable and, further, even the Cartesian product of two stars, which in a sense are the “most” unsolvable graphs.


2012 ◽  
Vol 160 (3) ◽  
pp. 210-217 ◽  
Author(s):  
Fatemeh Keshavarz-Kohjerdi ◽  
Alireza Bagheri ◽  
Asghar Asgharian-Sardroud

Author(s):  
Stuart Oldham ◽  
Aurina Arnatkevic̆iūtė ◽  
Robert E. Smith ◽  
Jeggan Tiego ◽  
Mark A. Bellgrove ◽  
...  

AbstractHead motion is a major confounding factor in neuroimaging studies. While numerous studies have investigated how motion impacts estimates of functional connectivity, the effects of motion on structural connectivity measured using diffusion MRI have not received the same level of attention, despite the fact that, like functional MRI, diffusion MRI relies on elaborate preprocessing pipelines that require multiple choices at each step. Here, we report a comprehensive analysis of how these choices influence motion-related contamination of structural connectivity estimates. Using a healthy adult sample (N = 252), we evaluated 240 different preprocessing pipelines, devised using plausible combinations of different choices related to explicit head motion correction, tractography propagation algorithms, track seeding methods, track termination constraints, quantitative metrics derived for each connectome edge, and parcellations. We found that an approach to motion correction that includes outlier replacement and within-slice volume correction led to a dramatic reduction in cross-subject correlations between head motion and structural connectivity strength, and that motion contamination is more severe when quantifying connectivity strength using mean tract fractional anisotropy rather than streamline count. We also show that the choice of preprocessing strategy can significantly influence subsequent inferences about network organization, with the location of network hubs varying considerably depending on the specific preprocessing steps applied. Our findings indicate that the impact of motion on structural connectivity can be successfully mitigated using recent motion-correction algorithms that include outlier replacement and within-slice motion correction.HighlightsWe assess how motion affects structural connectivity in 240 preprocessing pipelinesMotion contamination of structural connectivity depends on preprocessing choicesAdvanced motion correction tools reduce motion confoundsFA edge weighting is more susceptible to motion effects than streamline count


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