The number of Hamiltonian circuits

G = 〈V(G), E(G)〉 denotes a directed graph without loops and multiple arrows. K(G) denotes the set of all Hamiltonian circuits of G. Put H(n, r) = max{|E(G)|, |V(G)| = n, 1 ≤ |K(G)| ≤ r}. Theorem: H(n, 1) = (n22) + (n2) −1. Further, H(n, 2),…, H(n, 5) are given.