Secure Domination Cover Pebbling Number of Join of graphs

S Sarah Surya; Lian Mathew

doi:10.17485/IJST/v15i27.2145

Article

Secure Domination Cover Pebbling Number of Join of graphs

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v15i27.2145

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

Original Article

Secure Domination Cover Pebbling Number of Join of graphs

S Sarah Surya¹, Lian Mathew^1*

¹Department of Mathematics, Stella Maris College (Autonomous), Affiliated to the University of Madras, Chennai, India

*Corresponding Author
Email: [email protected]

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

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

Abstract

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

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Copyright

© 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)