RESEARCH ARTICLE

On square-Hamiltonian graphs

K. D. Protasova

Department of Cybernetics, Kyiv University, Volodimirska 64, Kyiv 01033, Ukraine

Abstract: A finite connected graph $G$ is called square-Hamiltonian if $G^{2}$ is Hamiltonian. We prove that any join of the family of Hamiltonian graphs by tree is square-Hamiltonian. Applying this statement we show that the line graph and any round-about reconstruction of an arbitrary finite connected graph is square-Hamiltonian.

Keywords: square-Hamiltonian graphs, join of graphs, line graph, round-about reconstruction.

MSC: 05C45

Received: 15.08.2005
Revised: 10.09.2005

Language: English

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