scholarly journals Optimal Pebbling Number of the Square Grid

2020 ◽  
Vol 36 (3) ◽  
pp. 803-829
Author(s):  
Ervin Győri ◽  
Gyula Y. Katona ◽  
László F. Papp
Keyword(s):  
Square Grid ◽  
Pebbling Number ◽  
Optimal Pebbling

scholarly journals The optimal pebbling number of staircase graphs

2019 ◽  
Vol 342 (7) ◽  
pp. 2148-2157 ◽  
Author(s):  
Ervin Győri ◽  
Gyula Y. Katona ◽  
László F. Papp ◽  
Casey Tompkins
Keyword(s):  
Pebbling Number ◽  
Optimal Pebbling

scholarly journals Constructions for the Optimal Pebbling of Grids

2017 ◽  
Vol 61 (2) ◽  
pp. 217 ◽  
Author(s):  
Ervin Győri ◽  
Gyula Y. Katona ◽  
László F. Papp
Keyword(s):  
Square Grid ◽  
Optimal Pebbling

In [6] the authors conjecture that if every vertex of an infinite square grid is reachable from a pebble distribution, then the covering ratio of this distribution is at most 3.25. First we present such a distribution with covering ratio 3.5, disproving the conjecture. The authors in the above paper also claim to prove that the covering ratio of any pebble distribution is at most 6.75. The proof contains some errors. We present a few interesting pebble distributions that this proof does not seem to cover and highlight some other difficulties of this topic.

scholarly journals THE OPTIMAL PEBBLING NUMBER OF THE CATERPILLAR

2009 ◽  
Vol 13 (2A) ◽  
pp. 419-429 ◽  
Author(s):  
Chin-Lin Shiue ◽  
Hung-Lin Fu
Keyword(s):  
Pebbling Number ◽  
Optimal Pebbling

scholarly journals The optimal pebbling number of the complete m-ary tree

2000 ◽  
Vol 222 (1-3) ◽  
pp. 89-100 ◽  
Author(s):  
Hung-Lin Fu ◽  
Chin-Lin Shiue
Keyword(s):  
Pebbling Number ◽  
Optimal Pebbling

scholarly journals Optimal pebbling number of graphs with given minimum degree

2019 ◽  
Vol 260 ◽  
pp. 117-130
Author(s):  
A. Czygrinow ◽  
G. Hurlbert ◽  
G.Y. Katona ◽  
L.F. Papp
Keyword(s):  
Minimum Degree ◽  
Pebbling Number ◽  
Optimal Pebbling

scholarly journals The optimal pebbling of spindle graphs

2019 ◽  
Vol 17 (1) ◽  
pp. 582-587
Author(s):  
Ze-Tu Gao ◽  
Jian-Hua Yin
Keyword(s):  
Connected Graph ◽  
Adjacent Vertex ◽  
Left Endpoint ◽  
Pebbling Number ◽  
The Right ◽  
Optimal Pebbling

Abstract Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move on G consists of taking two pebbles off one vertex and placing one on an adjacent vertex. The optimal pebbling number of G, denoted by πopt(G), is the smallest number m such that for some distribution of m pebbles on G, one pebble can be moved to any vertex of G by a sequence of pebbling moves. Let Pk be the path on k vertices. Snevily defined the n–k spindle graph as follows: take n copies of Pk and two extra vertices x and y, and then join the left endpoint (respectively, the right endpoint) of each Pk to x (respectively, y), the resulting graph is denoted by S(n, k), and called the n–k spindle graph. In this paper, we determine the optimal pebbling number for spindle graphs.

Cover Pebbling Number of Some Cycle Related Graphs

2019 ◽  
Vol 10 (6) ◽  
pp. 1322-1331
Author(s):  
Joice Punitha M ◽  
Suganya A
Keyword(s):  
Pebbling Number

scholarly journals Fractal-induced 2D flexible net undulation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michael Joon Seng Goh ◽  
Yeong Shiong Chiew ◽  
Ji Jinn Foo
Keyword(s):  
3D Reconstruction ◽  
Cross Section ◽  
Channel Cross Section ◽  
Time Varying ◽  
Blockage Ratio ◽  
Transient Time ◽  
Cross Sectional ◽  
Velocity Fluctuations ◽  
Square Grid ◽  
Multilength Scale

AbstractA net immersed in fractal-induced turbulence exhibit a transient time-varying deformation. The anisotropic, inhomogeneous square fractal grid (SFG) generated flow interacts with the flexible net to manifest as visible cross-sectional undulations. We hypothesize that the net’s response may provide a surrogate in expressing local turbulent strength. This is analysed as root-mean-squared velocity fluctuations in the net, displaying intensity patterns dependent on the grid conformation and grid-net separation. The net’s fluctuation strength is found to increase closer to the turbulator with higher thickness ratio while presenting stronger fluctuations compared to regular-square-grid (RSG) of equivalent blockage-ratio, σ. Our findings demonstrate a novel application where 3D-reconstruction of submerged nets is used to experimentally contrast the turbulence generated by RSG and multilength scale SFGs across the channel cross-section. The net’s response shows the unique turbulence developed from SFGs can induce 9 × higher average excitation to a net when compared against RSG of similar σ.

Chromous carbonates containing a square-grid layer of {Cr2(CO3)4}n4n− based on a dichromium(ii,ii) paddlewheel core

2021 ◽  
Vol 50 (7) ◽  
pp. 2387-2392
Author(s):  
Zhi-Qiang Dong ◽  
Jian-Hui Yang ◽  
Bin Liu
Keyword(s):  
Magnetic Properties ◽  
Layer Structure ◽  
Square Grid

The structural, spectroscopic and magnetic properties of chromous carbonates with a square-grid layer structure constructed from Cr2(CO3)44− paddlewheel units.

scholarly journals ON A FABRIC OF KISSING CIRCLES

2021 ◽  
pp. 1-10
Author(s):  
VIERA ČERŇANOVÁ
Keyword(s):  
Sufficient Condition ◽  
Arithmetic Sequence ◽  
Square Grid ◽  
The Individual

Abstract Applying circle inversion on a square grid filled with circles, we obtain a configuration that we call a fabric of kissing circles. We focus on the curvature inside the individual components of the fabric, which are two orthogonal frames and two orthogonal families of chains. We show that the curvatures of the frame circles form a doubly infinite arithmetic sequence (bi-sequence), whereas the curvatures in each chain are arranged in a quadratic bi-sequence. We also prove a sufficient condition for the fabric to be integral.

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