Geodesic
On square-Hamiltonian graphs
Algebra and discrete mathematics, no. 3 (2005), pp. 56-59

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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. 
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     author = {K. D. Protasova},
     title = {On {square-Hamiltonian} graphs},
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     number = {3},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2005_3_a4/}
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K. D. Protasova. On square-Hamiltonian graphs. Algebra and discrete mathematics, no. 3 (2005), pp. 56-59. http://geodesic.mathdoc.fr/item/ADM_2005_3_a4/