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Journal articles on the topic 'Pebbling'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

Ye, Yongsheng, Fang Liu, and Caixia Shi. "The 2-Pebbling Property of the Middle Graph of Fan Graphs." Journal of Applied Mathematics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/304514.

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A pebbling move on a graphGconsists of taking two pebbles off one vertex and placing one pebble on an adjacent vertex. The pebbling number of a connected graphG, denoted byf(G), is the leastnsuch that any distribution ofnpebbles onGallows one pebble to be moved to any specified but arbitrary vertex by a sequence of pebbling moves. This paper determines the pebbling numbers and the 2-pebbling property of the middle graph of fan graphs.

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2

Bunde, David P., Erin W. Chambers, Daniel Cranston, Kevin Milans, and Douglas B. West. "Pebbling and optimal pebbling in graphs." Journal of Graph Theory 57, no. 3 (2008): 215–38. http://dx.doi.org/10.1002/jgt.20278.

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3

Li, Yueqing, and Yongsheng Ye. "The 2-pebbling property of squares of paths and Graham’s conjecture." Open Mathematics 18, no. 1 (March 10, 2020): 87–92. http://dx.doi.org/10.1515/math-2020-0009.

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Abstract A pebbling move on a graph G consists of taking two pebbles off one vertex and placing one pebble on an adjacent vertex. The pebbling number of a connected graph G, denoted by f(G), is the least n such that any distribution of n pebbles on G allows one pebble to be moved to any specified vertex by a sequence of pebbling moves. In this paper, we determine the 2-pebbling property of squares of paths and Graham’s conjecture on $\begin{array}{} P_{2n}^2 \end{array} $.

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4

Moews, David. "Pebbling graphs." Journal of Combinatorial Theory, Series B 55, no. 2 (July 1992): 244–52. http://dx.doi.org/10.1016/0095-8956(92)90043-w.

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5

Lourdusamy, A., and T. Mathivanan. "Herscovici’s conjecture on C2n × G." Discrete Mathematics, Algorithms and Applications 12, no. 05 (July 1, 2020): 2050071. http://dx.doi.org/10.1142/s1793830920500718.

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The [Formula: see text]-pebbling number, [Formula: see text], of a connected graph [Formula: see text], is the smallest positive integer such that from every placement of [Formula: see text] pebbles, [Formula: see text] pebbles can be moved to any specified target vertex by a sequence of pebbling moves, each move taking two pebbles off a vertex and placing one on an adjacent vertex. A graph [Formula: see text] satisfies the [Formula: see text]-pebbling property if [Formula: see text] pebbles can be moved to any specified vertex when the total starting number of pebbles is [Formula: see text], where [Formula: see text] is the number of vertices with at least one pebble. We show that the cycle [Formula: see text] satisfies the [Formula: see text]-pebbling property. Herscovici conjectured that for any connected graphs [Formula: see text] and [Formula: see text], [Formula: see text]. We prove Herscovici’s conjecture is true, when [Formula: see text] is an even cycle and for variety of graphs [Formula: see text] which satisfy the [Formula: see text]-pebbling property.

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6

Cusack, Charles A., Airat Bekmetjev, and Mark Powers. "Two-pebbling and odd-two-pebbling are not equivalent." Discrete Mathematics 342, no. 3 (March 2019): 777–83. http://dx.doi.org/10.1016/j.disc.2018.10.030.

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7

Gao, Ze-Tu, and Jian-Hua Yin. "The optimal pebbling of spindle graphs." Open Mathematics 17, no. 1 (November 13, 2019): 582–87. http://dx.doi.org/10.1515/math-2019-0094.

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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.

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8

Chung, Fan, Ron Graham, John Morrison, and Andrew Odlyzko. "Pebbling a Chessboard." American Mathematical Monthly 102, no. 2 (February 1995): 113. http://dx.doi.org/10.2307/2975345.

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9

Chung, Fan, Ron Graham, John Morrison, and Andrew Odlyzko. "Pebbling a Chessboard." American Mathematical Monthly 102, no. 2 (February 1995): 113–23. http://dx.doi.org/10.1080/00029890.1995.11990546.

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10

Kirousis, Lefteris M., and Christos H. Papadimitriou. "Searching and pebbling." Theoretical Computer Science 47 (1986): 205–18. http://dx.doi.org/10.1016/0304-3975(86)90146-5.

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11

Chung, Fan R. K. "Pebbling in Hypercubes." SIAM Journal on Discrete Mathematics 2, no. 4 (November 1989): 467–72. http://dx.doi.org/10.1137/0402041.

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12

Chan, Melody, and Anant P. Godbole. "Improved pebbling bounds." Discrete Mathematics 308, no. 11 (June 2008): 2301–6. http://dx.doi.org/10.1016/j.disc.2006.06.032.

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13

Hurlbert, Glenn. "General graph pebbling." Discrete Applied Mathematics 161, no. 9 (June 2013): 1221–31. http://dx.doi.org/10.1016/j.dam.2012.03.010.

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14

Gao, Ze-Tu, and Jian-Hua Yin. "On thet-pebbling number and the2t-pebbling property of graphs." Discrete Applied Mathematics 161, no. 7-8 (May 2013): 999–1005. http://dx.doi.org/10.1016/j.dam.2012.12.005.

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15

Pleanmani, Nopparat. "Graham’s pebbling conjecture holds for the product of a graph and a sufficiently large complete bipartite graph." Discrete Mathematics, Algorithms and Applications 11, no. 06 (December 2019): 1950068. http://dx.doi.org/10.1142/s179383091950068x.

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A graph pebbling is a network optimization model for the transmission of consumable resources. A pebbling move on a connected graph [Formula: see text] is the process of removing two pebbles from a vertex and placing one of them on an adjacent vertex after configuration of a fixed number of pebbles on the vertex set of [Formula: see text]. The pebbling number of [Formula: see text], denoted by [Formula: see text], is defined to be the least number of pebbles to guarantee that for any configuration of pebbles on [Formula: see text] and arbitrary vertex [Formula: see text], there is a sequence of pebbling movement that places at least one pebble on [Formula: see text]. For connected graphs [Formula: see text] and [Formula: see text], Graham’s conjecture asserted that [Formula: see text]. In this paper, we show that such conjecture holds when [Formula: see text] is a complete bipartite graph with sufficiently large order in terms of [Formula: see text] and the order of [Formula: see text].

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16

Czygrinow, Andrzej, and Glenn H. Hurlbert. "On the pebbling threshold of paths and the pebbling threshold spectrum." Discrete Mathematics 308, no. 15 (August 2008): 3297–307. http://dx.doi.org/10.1016/j.disc.2007.06.045.

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17

Kim, Ju-Young, and Sun-Ah Kim. "PEBBLING EXPONENTS OF PATHS." Honam Mathematical Journal 32, no. 4 (December 25, 2010): 769–76. http://dx.doi.org/10.5831/hmj.2010.32.4.769.

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18

Lourdusamy, A., and S. Saratha Nellainayaki. "DETOUR PEBBLING IN GRAPHS." Advances in Mathematics: Scientific Journal 9, no. 12 (December 6, 2020): 10583–89. http://dx.doi.org/10.37418/amsj.9.12.44.

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19

Alcón, Liliana, Marisa Gutierrez, and Glenn Hurlbert. "Pebbling in 2-Paths." Electronic Notes in Discrete Mathematics 50 (December 2015): 145–50. http://dx.doi.org/10.1016/j.endm.2015.07.025.

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20

Wang, Stephen S. "Pebbling and Graham's Conjecture." Discrete Mathematics 226, no. 1-3 (January 2001): 431–38. http://dx.doi.org/10.1016/s0012-365x(00)00177-1.

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21

Alcón, Liliana, Marisa Gutierrez, and Glenn Hurlbert. "Pebbling in Split Graphs." SIAM Journal on Discrete Mathematics 28, no. 3 (January 2014): 1449–66. http://dx.doi.org/10.1137/130914607.

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22

Muntz, Jessica, Sivaram Narayan, Noah Streib, and Kelly Van Ochten. "Optimal pebbling of graphs." Discrete Mathematics 307, no. 17-18 (August 2007): 2315–21. http://dx.doi.org/10.1016/j.disc.2006.11.005.

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23

Herscovici, D. S., B. D. Hester, and G. H. Hurlbert. "t-Pebbling and Extensions." Graphs and Combinatorics 29, no. 4 (March 24, 2012): 955–75. http://dx.doi.org/10.1007/s00373-012-1152-4.

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24

Xue, Chenxiao, and Carl Yerger. "Optimal Pebbling on Grids." Graphs and Combinatorics 32, no. 3 (August 9, 2015): 1229–47. http://dx.doi.org/10.1007/s00373-015-1615-5.

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25

Tamilselvi, B. "Pebbling Graphs of Various Diameter." IOSR Journal of Mathematics 10, no. 5 (2014): 24–38. http://dx.doi.org/10.9790/5728-10552438.

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26

S, Ms Sreedevi, and Dr M. S. Anilkumar. "Pebbling In Watkins Snark Graph." International Journal of Research in Advent Technology 7, no. 2 (March 10, 2019): 247–52. http://dx.doi.org/10.32622/ijrat.72201964.

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27

Hurlbert, Glenn. "On the Pebbling Threshold Spectrum." Electronic Notes in Discrete Mathematics 10 (November 2001): 146–50. http://dx.doi.org/10.1016/s1571-0653(04)00381-6.

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28

Moews, David. "Optimally pebbling hypercubes and powers." Discrete Mathematics 190, no. 1-3 (August 1998): 271–76. http://dx.doi.org/10.1016/s0012-365x(98)00154-x.

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29

Knessl, C. "Geometrical optics and chessboard pebbling." Applied Mathematics Letters 14, no. 3 (April 2001): 365–73. http://dx.doi.org/10.1016/s0893-9659(00)00163-4.

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30

Lourdusamy, A., and S. Somasundaram. "Pebbling C5× C5using linear programming." Journal of Discrete Mathematical Sciences and Cryptography 4, no. 1 (April 2001): 1–15. http://dx.doi.org/10.1080/09720529.2001.10697915.

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31

Postle, Luke. "Pebbling Graphs of Fixed Diameter." Journal of Graph Theory 75, no. 4 (February 21, 2013): 302–10. http://dx.doi.org/10.1002/jgt.21736.

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32

Milans, Kevin, and Bryan Clark. "The Complexity of Graph Pebbling." SIAM Journal on Discrete Mathematics 20, no. 3 (January 2006): 769–98. http://dx.doi.org/10.1137/050636218.

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33

Czygrinow, Andrzej, and Glenn Hurlbert. "Girth, Pebbling, and Grid Thresholds." SIAM Journal on Discrete Mathematics 20, no. 1 (January 2006): 1–10. http://dx.doi.org/10.1137/s0895480102416374.

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34

Feng, Rongquan, and Ju Young Kim. "Pebbling numbers of some graphs." Science in China Series A: Mathematics 45, no. 4 (April 2002): 470–78. http://dx.doi.org/10.1007/bf02872335.

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35

Czygrinow, Andrzej, Glenn Hurlbert, H. A. Kierstead, and William T. Trotter. "A Note on Graph Pebbling." Graphs and Combinatorics 18, no. 2 (May 1, 2002): 219–25. http://dx.doi.org/10.1007/s003730200015.

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36

Herscovici, David S., Benjamin D. Hester, and Glenn H. Hurlbert. "Generalizations of Graham’s pebbling conjecture." Discrete Mathematics 312, no. 15 (August 2012): 2286–93. http://dx.doi.org/10.1016/j.disc.2012.03.032.

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37

Gao, Ze-Tu, and Jian-Hua Yin. "Thet-pebbling number ofC5□C5." Discrete Mathematics 313, no. 23 (December 2013): 2778–91. http://dx.doi.org/10.1016/j.disc.2013.08.024.

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38

Alcón, Liliana, Marisa Gutierrez, and Glenn Hurlbert. "Pebbling in semi-2-trees." Discrete Mathematics 340, no. 7 (July 2017): 1467–80. http://dx.doi.org/10.1016/j.disc.2017.02.011.

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39

Srinivasan, Sakunthala, and Vimala Shanmugavel. "Adjacency energy of pebbling graphs." Journal of Physics: Conference Series 1850, no. 1 (May 1, 2021): 012089. http://dx.doi.org/10.1088/1742-6596/1850/1/012089.

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40

Herscovici, David S., and Aparna W. Higgins. "The pebbling number of C5 × C5." Discrete Mathematics 187, no. 1-3 (June 1998): 123–35. http://dx.doi.org/10.1016/s0012-365x(97)00229-x.

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41

Bekmetjev, Airat, and Charles A. Cusack. "Pebbling Algorithms in Diameter Two Graphs." SIAM Journal on Discrete Mathematics 23, no. 2 (January 2009): 634–46. http://dx.doi.org/10.1137/080724277.

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42

Ružička, Peter, and Juraj Waczulík. "Pebbling dynamic graphs in minimal space." RAIRO - Theoretical Informatics and Applications 28, no. 6 (1994): 557–65. http://dx.doi.org/10.1051/ita/1994280605571.

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43

Lourdusamy, A., and C. Muthulakshmi. "Generalizedt-pebbling number of a graph." Journal of Discrete Mathematical Sciences and Cryptography 12, no. 1 (February 2009): 109–20. http://dx.doi.org/10.1080/09720529.2009.10698222.

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44

冯, 荣权, and 珠英金. "几类图的pebbling数." Science in China Series A-Mathematics (in Chinese) 32, no. 3 (March 1, 2002): 197–204. http://dx.doi.org/10.1360/za2002-32-3-197.

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45

Crull, Betsy, Tammy Cundiff, Paul Feltman, Glenn H. Hurlbert, Lara Pudwell, Zsuzsanna Szaniszlo, and Zsolt Tuza. "The cover pebbling number of graphs." Discrete Mathematics 296, no. 1 (June 2005): 15–23. http://dx.doi.org/10.1016/j.disc.2005.03.009.

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46

Shiue, Chin-Lin. "Capacity restricted optimal pebbling in graphs." Discrete Applied Mathematics 260 (May 2019): 284–88. http://dx.doi.org/10.1016/j.dam.2019.01.002.

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47

Cusack, Charles A., Aaron Green, Airat Bekmetjev, and Mark Powers. "Graph pebbling algorithms and Lemke graphs." Discrete Applied Mathematics 262 (June 2019): 72–82. http://dx.doi.org/10.1016/j.dam.2019.02.028.

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48

Shiue, Chin-Lin. "Distance restricted optimal pebbling in cycles." Discrete Applied Mathematics 279 (May 2020): 125–33. http://dx.doi.org/10.1016/j.dam.2019.10.017.

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49

Fellner, Andreas, and Bruno Woltzenlogel Paleo. "Greedy pebbling for proof space compression." International Journal on Software Tools for Technology Transfer 21, no. 1 (June 27, 2017): 71–86. http://dx.doi.org/10.1007/s10009-017-0459-0.

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50

Gao, Ze-Tu, and Jian-Hua Yin. "Lemke graphs and Graham’s pebbling conjecture." Discrete Mathematics 340, no. 9 (September 2017): 2318–32. http://dx.doi.org/10.1016/j.disc.2016.09.004.

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