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A Family of Trivalent 1-Hamiltonian Graphs

With diameter

**Jeng-Jung Wang, Ting-Yi Sung ^{*} and Lih-Hsing Hsu**

National Chiao Tung University

Hsinchu, Taiwan 300, R.O.C.

E-mail: lhhsu@cc.nctu.edu.tw

Academia Sinica

Taipei, Taiwan 115, R.O.C.

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 O(log n), where n is the number of vertices in the graph and to be precise, n = 6(2s - 1) vertices.

Keywords: hamiltonian, edge hamiltonian, 1-vertex hamiltonian, 1-edge hamiltonian, 1-hamiltonian, diameter, Moore bound

Retrieve PDF document (**200107_01.pdf**)

Received April 30, 1999; revised December 17, 1999; accepted February 24, 2000.

Communicated by Jang-Ping Sheu.