On Pitchfork Domination Number of Corona of Some Graphs

A dominating set \(D\) of \(V\) is called a pitchfork dominating set if every vertex in it dominates at least \(j\) vertices and at most \(k\) vertices of \(V-D\), for any non-negative integers \(j\) and \(k\). The pitchfork domination number of \(G\), denoted by \(\gamma_{pf} (G)\) is the minimum cardinality over all pitchfork dominating sets in \(G\). In this paper, the pitchfork domination when \(j=1\) and \(k=2\) are applied to the corona of some graphs: \(G \circ C_m\), \(G \circ K_{1,n}\), \(G \circ K_{p,q}\), \(G \circ B_{2,k}\) and \(G \circ F_{2,k}\). In relation to getting new results of the corona of the mentioned graphs, we also generate results of pitchfork domination number of \(P_2+\overline{K}_n\), \(K_1 + K_{p,q}\), \(B_{2,k}\), \(F_{2,k}\) and \(K_1 + F_{2,k}\).