“…Therefore, it does not come as a surprise to hear that a great many efforts have been put into the enumeration of Hamiltonian paths and cycles for some lattices such as the rectangular grid graphs P m × P n , thin grid cylinder graphs C m × P n+1 and their triangular versions. Some of the papers devoted to this topic make use of coding the vertices of the graphs [2,11,12,13,16], whereas others prefer coding the square or triangular cells of the considered graph [1,3,4,5,15,17,19,20]. Nevertheless, common to almost all of them is the transfer matrix method [6,18] which is also being used here.…”