Secure Domination Cover Pebbling Number for Variants of Complete Graphs

On Secure Total Domination Cover Pebbling Number

“…We need a minimum of p + q + 8 pebbles to place a pebble on each of the vertices of the target vertex set by a pebbling move. The detailed proof is discussed in [10]. Theorem 4.4.…”

“…Now, we are left with q+5 pebbles and it is sufficient to place a pebble on each of the non-pebbled vertices in the newly obtained target vertex set. The detailed proof is mentioned in [10].…”

Secure Domination Cover Pebbling Number of Join of graphs

“…(1) f(P_{t+1})=2^t Result 2. (3) f_{sdp}(G)=1 iff G is complete graph Notation:p(v) denotes the number of pebbles placed at the vertex v.…”

“…Secure domination cover pebbling number is combination of cover pebbling and secure domination number. Secure domination cover pebbling number, f sd p (G), of a graph G is 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 regardless of the initial configuration (3) . It has wide applications; for instance, by using the concept of secure domination cover pebbling number we can find the minimum number of guards that are required to protect a country.…”

“…It has wide applications; for instance, by using the concept of secure domination cover pebbling number we can find the minimum number of guards that are required to protect a country. The detailed application of secure domination cover pebbling number is mentioned in (3) . In this paper, the secure domination cover pebbling number for the join of two graphs is determined and also generalization for the secure domination cover pebbling number of path P n is found.…”