Brother trees: a family of optimal 1p-Hamiltonian and 1-edge Hamiltonian graphs

Authors:
Shin-Shin Kao;Lih-Hsing Hsu
Affiliations:
Department of Applied Mathematics, Chung-Yuan Christian University, Chong-Li City 320, Taiwan, R.O.C.;Department of Computer and Information Science, National Chiao Tung University, Hsinchu 300, Taiwan, R.O.C.
Venue:
Information Processing Letters
Year:
2003

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Abstract

In this paper we propose a family of cubic bipartite planar graphs, brother trees, denoted by BT(n) with n ≥ 2. Any BT(n) is Hamiltonian. It remains Hamiltonian if any edge is deleted. Moreover, it remains Hamiltonian when a pair of nodes (one from each partite set) is deleted. These properties are optimal. Furthermore, the number of nodes in BT(n) is 6 ċ 2n - 4 and the diameter is 2n + 1.