Super Restrained Domination in the Join of Some Graphs - Lorono, Monrille L.; Espinola, Stephanie O. (Communications in Mathematics and Applications, 2024)
Let \(G=(V(G),E(G))\) be a simple graph. A set \(SV(G)\) is a restrained dominating set \(S\) if every vertex not in \(S\) is adjacent to a vertex in \(S\) and to a vertex in \(V(G)S\). It is a super restrained dominating set if for every vertex \(uV(G)S\), there exists \(vS\) such that \(N_G(v)(V(G)S)={u }\). The minimum cardinality of a super restrained dominating set in \(G\), denoted by \(γ _spr (G)\), is called the super restrained domination number of \(G\). In this paper, the researchers obtained the super restrained domination number of the following graphs: \(F_nK_1+P_n\), \(W_nK_1+C_n\), \(S_nK_1+K_n\), \(D^(m)_nK_1+mK_n-1\) and \(K_m,nK_m+K_n\).