A family of trivalent 1-hamiltonian graphs with diameter O(log n)

Abstract

In this paper, we construct a family of graphs denoted by Eye(s) that are 3-regular, 3-connected, planar, hamiltonian, edge hamiltonian, and also minimal 1-hamiltonian. Furthermore, the diameter of Eye(s) is 0(log n), where n is the number of vertices in the Mph and to be precise, n = 6(2(s) - 1) vertices.