All graphs in this article are finite, undirected, without loops or multiple edges. Let \(G\) be a graph with vertices \(v_1,v_2,\dots, v_n\). The complement in \(G\) of a subgraph \(H\) is the subgraph of \(G\) obtained by deleting all edges in \(H\). The join \(G_1\vee G_2\) of two graphs \(G_1\) and \(G_2\) is obtained by adding an edge from each vertex in \(G_1\) to each vertex in \(G_2\). Let \(K_n\) be the complete graph and \(P_n\) the path on \(n\) vertices. The concept Fibonacci number \(f\) of a simple graph \(G\) refers to the number of subsets \(S\) of \(V(G)\) such that no two vertices in \(S\) are adjacent [H. Prodinger and R. F. Tichy, Fibonacci Q. 20, No. 1, 16-21 (1982; Zbl 0475.05046)]. Accordingly, the total number of subsets of \(\{1,2,\dots, n\}\) such that no two elements are adjacent is \(F_{n+1}\), the \((n+1)\)th Fibonacci number.