On Secure Total Domination Cover Pebbling Number

Authors

DOI:

https://doi.org/10.26713/cma.v13i1.1690

Keywords:

Graph pebbling, Secure total domination, Cover pebbling number, Secure total domination cover pebbling number

Abstract

In this paper, we introduce a new graph invariant called the secure total domination cover pebbling number, a combination of two graph invariants, namely, `secure total domination' and `cover pebbling number'. The secure total domination cover pebbling number of a graph \(G\), denoted by \(f_{stdp}(G)\), is the minimum number of pebbles that are required to place on \(V(G)\), such that after a sequence of pebbling moves, the set of vertices with pebbles forms a total secure dominating set under any configuration of pebbles to the vertices of graph \(G\). The secure total domination cover pebbling number for join of two graphs \(G(p,q)\) and \(G'(p',q')\) is determined. Also, a generalization of secure total domination cover pebbling number for some families of graphs such as complete graph \(K_n\), complete bipartite graph \(K_{p,q}\), complete $y$-partite graph \(K_{p_1,p_2,\ldots,p_y}\) and path \(P_n\) is found.

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References

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Published

23-05-2022
CITATION

How to Cite

Surya, S. S., & Mathew, L. (2022). On Secure Total Domination Cover Pebbling Number. Communications in Mathematics and Applications, 13(1), 117–127. https://doi.org/10.26713/cma.v13i1.1690

Issue

Vol. 13 No. 1 (2022)

Section

Research Article

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