Maximal matching cover pebbling number for variants of hypercube

Authors

  • S. Sarah Surya Stella Maris College (Autonomous).
  • Lian Mathew Koipuram CHRIST (Deemed to be University).

DOI:

https://doi.org/10.22199/issn.0717-6279-5608

Keywords:

graph pebbling, maximal matching, cover pebbling number, maximal matching cover pebbling number

Abstract

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.

Author Biographies

S. Sarah Surya, Stella Maris College (Autonomous).

Department of Mathematics.

Lian Mathew Koipuram, CHRIST (Deemed to be University).

Research Scholar.

References

J. A. Bondy and US Murty, Graph theory with applications. London: Macmillan, 1976.

X. Cai and E. Vumar, “The super connectivity of folded crossed cubes”, Information Processing Letters, vol. 142, pp. 52-56, 2019. https://doi.org10.1016/j.ipl.2018.10.013

F. R. K. Chung, “Pebbling in hypercubes”, SIAM Journal on Discrete Mathematics, vol. 2, no. 4, pp. 467-472, 1989. https://doi.org10.1137/0402041

B. Crull, T. Cundiff, P. Feltman, GH. Hurlbert, L. Pudwell, Z. Szaniszlo and Z. Tuza, “The cover pebbling number of graphs”, Discrete mathematics, vol. 296, no. 1, pp. 15-23, 2005.

J. Gardner, A.P. Godbole, A.M. Teguia, A.Z. Vuong, N. Watson and C.R. Yerger, “Domination cover pebbling: graph families”, Journal of Combinatorial Mathematics and Combinatorial Computin, vol. 64, pp. 255-271, 2008.

G.H. Hurlbert, “A survey of graph pebbling”, Congressus Numerantium, vol. 139, pp. 41-64, 1999.

A. P. Paul, “On Edge Pebbling Number and Cover Edge Pebbling Number of Some Graphs”, Journal of Information and Computational Science, vol. 10, no. 6, pp. 337-344, 2020.

T. L. Holt, J.E. Worley and A.P. Godbole, Explorations in domination cover pebbling. Preprint.

S. Sarah and L. Mathew, “On Maximal Matching Cover Pebbling Number”, Advances ad Applications in Mathematical Sciences, vol. 21, no. 11, pp. 6281-6302, 2022.

S. Sarah and L. Mathew, “On Total Secure Domination Cover Pebbling Number”, Communications in Mathematics and Applications, vol. 13, no. 1, pp. 117-127, 2022.

S. Sarah and L. Mathew, “Secure Domination Cover Pebbling Number for Variants of Complete Graphs”, Advances and Applications in Discrete Mathematics, vol. 27, no. 1, pp. 105-122, 2021. https://doi.org10.17654/dm027010105

Published

2023-07-18

How to Cite

[1]
S. Sarah Surya and L. . Mathew Koipuram, “Maximal matching cover pebbling number for variants of hypercube”, Proyecciones (Antofagasta, On line), vol. 42, no. 4, pp. 931-956, Jul. 2023.

Issue

Vol. 42 No. 4 (2023)

Section

Artículos

Copyright (c) 2023 S. Sarah Surya, Lian Mathew Koipuram

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.