A total perfect dominating set of a graph G, denoted by γ (????), is a subset S of its ???????? vertex set V(G) that satisfies two conditions: first, it is a total dominating set, meaning every vertex in the graph is either in S or adjacent to a vertex in S. Second, it is a perfect dominating set, meaning every vertex not in S has at least one neighbor in S. The total perfect domination number, γ (????), is the cardinality of the smallest total perfect dominating set in G. A γ − ???????????? of ???????? ???????? G is a total perfect dominating set of G that has cardinality equal to γ (????).