A Family of Trivalent 1-Hamiltonian Graphs With Diameter O(log n)
Jeng-Jung Wang, Ting‐Yi Sung, Lih‐Hsing Hsu · 2001
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) isO(log n), where n is the number of vertices in the graph and to be precise, n =6(2 s − 1) vertices.