On Secure Total Domination Cover Pebbling Number - Surya, S. Sarah; Mathew, Lian (Communications in Mathematics and Applications, 2022)
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 \(K_p_1,p_2,…,p_y\) and path \(P_n\) is found.