A New Family of Optimal 1-Hamiltonian Graphs with Small Diameter

Authors:
Jeng-Jung Wang;Ting-Yi Sung;Lih-Hsing Hsu;Men-Yang Lin
Affiliations:
-;-;-;-
Venue:
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
Year:
1998

Citing 3
Cited 0

Hamiltonian graphs with minimum number of edges for fault-tolerant topologies

Information Processing Letters
Optimal 1-Hamiltonian graphs

Information Processing Letters
Graph Theory With Applications

Graph Theory With Applications

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Abstract

In this paper, we construct a family of graphs denoted by Eye(s) that are 3-regualr, 3-connected, planar, hamiltonian, edge hamiltonian, and also optimal 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.