• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2022, Volume: 15, Issue: 27, Pages: 1344-1348

Original Article

Secure Domination Cover Pebbling Number of Join of graphs

Received Date:18 November 2021, Accepted Date:21 June 2022, Published Date:14 July 2022


Objectives: To find the secure domination cover pebbling number for the join of two graphs G(p; q) and G ′ (p ′ ;q ′ ). Methods: 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. Findings: We found the secure domination cover pebbling number for the join of two graphs G(p; q) and Kn. Also, the secure domination cover pebbling number for the join of two graphs G(p; q) and G ′ (p ′ ;q ′ ) is determined when the cardinality of the secure dominating set is 2, 3 and 4. A generalization for the secure domination cover pebbling number of path Pn is also found. Subject Mathematics Classification: 05C38, 05C69

Keywords: Graph pebbling; Secure domination; Cover pebbling number; Secure domination cover pebbling number 2010 Subject Mathematics Classification: 05C38; 05C69


  1. Chung FR. Pebbling in Hypercubes. SIAM Journal on Discrete Mathematics. 1989;2(4):467–472. Available from: https://doi.org/10.1137/0402041
  2. Hurlbert GH. A survey of graph pebbling. In Congr. Numer. 1999;139:41–64.
  3. Surya SS, Mathew L. Secure Domination Cover Pebbling Number for Variants of Complete Graphs. Advances and Applications in Discrete Mathematics. 2021;27(1):105–122. Available from: http://dx.doi.org/10.17654/DM027010105
  4. Gardner J, Godbole AP, Teguia AM, Vuong AZ, Watson N, Yerger CR. Domination cover pebbling: graph families. JCMCC . 2008;64:255–271.
  5. Crull B, Cundiff T, Feltman P, Hurlbert GH, Pudwell L, Szaniszlo Z, et al. The cover pebbling number of graphs. Discrete mathematics. 2005;296:15–23. Available from: https://doi.org/10.1016/j.disc.2005.03.009
  6. Bondy JA, Murty USR. Graph Theory with Applications. London: Macmillan. Macmillan Education UK. 1976.
  7. Castillano EC, Ugbinada RAL, Jr. SRC. Secure domination in the joins of graphs. Applied Mathematical Sciences. 2014;8(105):5203–5211. Available from: https://doi.org/10.12988/AMS.2014.47519


© 2022 Surya & Mathew. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Published By Indian Society for Education and Environment (iSee)


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