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Journal articles on the topic 'Cover pebbling'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

S, Sarah Surya, and Mathew Lian. "Secure Domination Cover Pebbling Number of Join of graphs." Indian Journal of Science and Technology 15, no. 27 (2022): 1344–48. https://doi.org/10.17485/IJST/v15i27.2145.

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Abstract <strong>Objectives:</strong> To find the secure domination cover pebbling number for the join of two graphs G(p; q) and G ′ (p ′ ;q ′ ). <strong>Methods:</strong> We define Secure domination cover pebbling number, fsd p(G), of a graph G as the minimum number of pebbles that must be placed on V(G) such that, after a sequence of pebbling moves, the set of vertices with pebbles forms a secure dominating set for G. <strong>Findings:</strong> We found the secure domination cover pebbling number for the join of two graphs G(p; q) and Kn. Also, the

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2

Priscilla, Paul, and Syed Ali Fathima S. "A Study on Edge Pebbling Number, Covering Cover Edge Pebbling Number of Friendship Graphs, Odd Path and Even Path." Indian Journal of Science and Technology 16, no. 32 (2023): 2480–84. https://doi.org/10.17485/IJST/v16i32.674.

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Abstract <strong>Objectives:</strong> To find the edge pebbling number and covering cover edge pebbling number of friendship graphs.<strong> Methods:</strong> The possible minimum edge covering set of the friendship graph is considered and the set with the minimum pebble requirement covering all vertices is selected. <strong>Findings:</strong> Obtained the modified result of edge pebbling number of friendship graph, defined the covering cover edge pebbling number of a graph G, and covering cover edge pebbling number for friendship graphs, odd path and even path is foun

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3

Lourdusamy, A., F. Joy Beaula, and F. Patrick. "Hub Cover Pebbling Number." Ars Combinatoria 160, no. 1 (2024): 31–35. http://dx.doi.org/10.61091/ars-160-05.

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The hub cover pebbling number, h ∗ ( G ) , of a graph $G$, is the least non-negative integer such that from all distributions of h ∗ ( G ) pebbles over the vertices of G , it is possible to place at least one pebble each on every vertex of a set of vertices of a hub set for G using a sequence of pebbling move operations, each pebbling move operation removes two pebbles from a vertex and places one pebble on an adjacent vertex. Here we compute the hub cover pebbling number for wheel related graphs.

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4

Sarah Surya, S., and Lian Mathew. "Maximal matching cover pebbling number for variants of hypercube." Proyecciones (Antofagasta) 42, no. 4 (2023): 931–56. http://dx.doi.org/10.22199/issn.0717-6279-5608.

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An edge pebbling move is defined as the removal of two pebbles from one edge and placing one on the adjacent edge. The maximal matching cover pebbling number, fmmcp(G), of a graph G, is the minimum number of pebbles that must be placed on E(G), such that after a sequence of pebbling moves the set of edges with pebbles forms a maximal matching regardless of the initial configuration. In this paper, we find the maximal matching cover pebbling number for variants of hypercube.

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5

Surya, S. Sarah, Lian Mathew, Jyothy Thomas, and Jeet Kurian Mattam. "SECURE VERTEX COVER PEBBLING NUMBER FOR FAMILIES OF TREE-DERIVED STRUCTURES." Advances and Applications in Discrete Mathematics 42, no. 2 (2024): 177–90. https://doi.org/10.17654/0974165825012.

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The secure vertex cover pebbling number of a graph , is the smallest number that allows every distribution of pebbles to reach some secure vertex cover of by a sequence of pebbling moves. Trees are advantageous in biological science especially in systematics, bioinformatics and phylogenetics. In this paper, the secure vertex cover pebbling number for some tree-derived structures such as coconut tree, comb graph, Bistar graph, Banana tree and complete binary tree has been determined.

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6

Lourdusamy, A. "On Binary DCP Labeling." Journal of Combinatorial Mathematics and Combinatorial Computing 122, no. 1 (2024): 255–61. http://dx.doi.org/10.61091/jcmcc122-21.

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A graph labeling is an assignment of integers to the vertices or edges or both, which satisfies certain conditions. The domination cover pebbling number of a graph G is ψ ( G ) , which is the minimum number of pebbles required such that any initial configuration of ψ ( G ) pebbles can be transformed through a number of pebbling moves so that the set of vertices with pebbles after the pebbling operation forms a dominating set of G . In this paper, we explore the relationship between two graph parameters, namely graph labeling and domination cover pebbling.

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7

Lourdusamy, A., S. Kither Iammal, and I. Dhivviyanandam. "Monophonic Cover Pebbling Number \((MCPN)\) of Network Graphs." Utilitas Mathematica 121, no. 1 (2024): 11–24. https://doi.org/10.61091/um121-02.

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Given a connected graph \(G\) and a configuration \(D\) of pebbles on the vertices of \(G\), a pebbling transformation involves removing two pebbles from one vertex and placing one pebble on its adjacent vertex. A monophonic path is defined as a chordless path between two non-adjacent vertices \(u\) and \(v\). The monophonic cover pebbling number, \(\gamma_{\mu}(G)\), is the minimum number of pebbles required to ensure that, after a series of pebbling transformations using monophonic paths, all vertices of \(G\) are covered with at least one pebble each. In this paper, we determine the monopho

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8

Lourdusamy, A., and T. Mathivanan. "The covering cover pebbling number for some acyclic graphs." Utilitas Mathematica 122 (March 30, 2025): 41–52. https://doi.org/10.61091/um122-03.

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The covering cover pebbling number, \(\sigma(G)\), of a graph \(G\), is the smallest number such that some distribution \(D \in \mathscr{K}\) is reachable from every distribution starting with \(\sigma(G)\) (or more) pebbles on \(G\), where \(\mathscr{K}\) is a set of covering distributions. In this paper, we determine the covering cover pebbling number for two families of graphs those do not contain any cycles.

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9

Crull, Betsy, Tammy Cundiff, Paul Feltman, et al. "The cover pebbling number of graphs." Discrete Mathematics 296, no. 1 (2005): 15–23. http://dx.doi.org/10.1016/j.disc.2005.03.009.

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10

Surya, S. Sarah, and Lian Mathew. "Secure Domination Cover Pebbling Number of Join of graphs." Indian Journal Of Science And Technology 15, no. 27 (2022): 1344–48. http://dx.doi.org/10.17485/ijst/v15i27.2145.

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11

Lourdusamy, A., I. Dhivviyanandam, and Lian Mathew. "NDC Pebbling Number for Some Class of Graphs." Journal of Combinatorial Mathematics and Combinatorial Computing 119, no. 1 (2024): 121–28. http://dx.doi.org/10.61091/jcmcc119-13.

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Let \(G\) be a connected graph. A pebbling move is defined as taking two pebbles from one vertex and the placing one pebble to an adjacent vertex and throwing away the another pebble. A dominating set \(D\) of a graph \(G=(V,E)\) is a non-split dominating set if the induced graph \(\) is connected. The Non-split Domination Cover(NDC) pebbling number, \(\psi_{ns}(G)\), of a graph $G$ is the minimum of pebbles that must be placed on \(V(G)\) such that after a sequence of pebbling moves, the set of vertices with a pebble forms a non-split dominating set of \(G\), regardless of the initial configu

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12

Surya, S. Sarah, and Lian Mathew. "On Secure Total Domination Cover Pebbling Number." Communications in Mathematics and Applications 13, no. 1 (2022): 117–27. http://dx.doi.org/10.26713/cma.v13i1.1690.

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13

Godbole, Anant P., Nathaniel G. Watson, and Carl R. Yerger. "Cover Pebbling Thresholds for the Complete Graph." Electronic Notes in Discrete Mathematics 22 (October 2005): 301–4. http://dx.doi.org/10.1016/j.endm.2005.06.046.

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14

Paul, Priscilla, and S. Syed Ali Fathima. "A Study on Edge Pebbling Number, Covering Cover Edge Pebbling Number of Friendship Graphs, Odd Path and Even Path." Indian Journal Of Science And Technology 16, no. 32 (2023): 2480–84. http://dx.doi.org/10.17485/ijst/v16i32.674.

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15

M, Joice Punitha, and Suganya A. "Cover Pebbling Number of Some Cycle Related Graphs." Journal of Computer and Mathematical Sciences 10, no. 6 (2019): 1322–31. http://dx.doi.org/10.29055/jcms/1127.

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16

Győri, Ervin, Gyula Y. Katona, and László F. Papp. "Constructions for the Optimal Pebbling of Grids." Periodica Polytechnica Electrical Engineering and Computer Science 61, no. 2 (2017): 217. http://dx.doi.org/10.3311/ppee.9724.

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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.

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17

Prabha, R., and B. Sandhiya. "Cover pebbling number of Comb, Friendship and Helm graphs." Journal of Physics: Conference Series 1770, no. 1 (2021): 012064. http://dx.doi.org/10.1088/1742-6596/1770/1/012064.

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18

Lourdusamy, A., S. Kither iammal, and I. Dhivviyanandam. "Monophonic Cover Pebbling Number of Standard and Algebraic Graphs." Communications in Mathematics and Applications 15, no. 2 (2024): 619–34. https://doi.org/10.26713/cma.v15i2.2625.

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19

Godbole, Anant P., Nathaniel G. Watson, and Carl R. Yerger. "Threshold and complexity results for the cover pebbling game." Discrete Mathematics 309, no. 11 (2009): 3609–24. http://dx.doi.org/10.1016/j.disc.2007.12.067.

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20

Surya, S. Sarah, and Lian Mathew. "SECURE DOMINATION COVER PEBBLING NUMBER FOR VARIANTS OF COMPLETE GRAPHS." Advances and Applications in Discrete Mathematics 27, no. 1 (2021): 105–22. http://dx.doi.org/10.17654/dm027010105.

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21

Subido, Michael E., and Imelda S. Aniversario. "The cover pebbling number of the join of some graphs." Applied Mathematical Sciences 8 (2014): 4275–83. http://dx.doi.org/10.12988/ams.2014.45377.

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22

Sjöstrand, Jonas. "The Cover Pebbling Theorem." Electronic Journal of Combinatorics 12, no. 1 (2005). http://dx.doi.org/10.37236/1989.

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For any configuration of pebbles on the nodes of a graph, a pebbling move replaces two pebbles on one node by one pebble on an adjacent node. A cover pebbling is a move sequence ending with no empty nodes. The number of pebbles needed for a cover pebbling starting with all pebbles on one node is trivial to compute and it was conjectured that the maximum of these simple cover pebbling numbers is indeed the general cover pebbling number of the graph. That is, for any configuration of this size, there exists a cover pebbling. In this note, we prove a generalization of the conjecture. All previous

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23

Lourdusamy, A., and T. Mathivanan. "Covering cover pebbling number for square of a path." Gulf Journal of Mathematics 2, no. 2 (2014). http://dx.doi.org/10.56947/gjom.v2i2.199.

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Let G be a connected graph. Let p be the number of pebbles distributed on the vertices of G. A pebbling move is defined by removing two pebbles from one vertex and put a pebble on an adjacent vertex. The covering cover pebbling number, σ(G), is the least p such that after a sequence of pebbling moves, the set of vertices should form a covering for G from every configuration of p pebbles on the vertices of G. In this paper, we determine the covering cover pebbling number for square of a path.

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24

A.Lourdusamy and T.Mathivanan. "Cover Pebbling Number for Square of a Path." August 20, 2012. https://doi.org/10.5281/zenodo.823963.

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25

Hurlbert, Glenn H., Lian Mathew, Jasintha Quadras, and S. Sarah Surya. "On the Secure Vertex Cover Pebbling Number." Asian-European Journal of Mathematics, July 14, 2023. http://dx.doi.org/10.1142/s1793557123501826.

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26

Xia, Zheng-Jiang, and Zhen-Mu Hong. "Generalization of the Cover Pebbling Number for Networks." Frontiers in Physics 8 (June 16, 2020). http://dx.doi.org/10.3389/fphy.2020.00197.

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27

Kavitha, K. C., S. Jagatheswari, I. Dhivviyanandam, and J. R. Prashitha. "Topological Properties and Computation of Neural Networks Using Cover Pebbling Number Technique with an Algorithmic Approach." Circuits, Systems, and Signal Processing, June 14, 2025. https://doi.org/10.1007/s00034-025-03201-x.

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28

Abramsky, Samson, and Luca Reggio. "Arboreal Categories: An Axiomatic Theory of Resources." Logical Methods in Computer Science Volume 19, Issue 3 (August 10, 2023). http://dx.doi.org/10.46298/lmcs-19(3:14)2023.

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Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures. In this paper, we develop a framework whereby the essential properties of these categories of coalgebras are captured in a purely axiomatic fashion. To this end, we introduce arboreal categories, which have an intrinsic process structure, allowing dynamic notions such as bisimulation and back-and-forth games, and resource notions such as number of rounds of a game, to be defined. These are related to extensional

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