Geodesic
Hamiltonian Cycles in Squares of Vertex-Unicyclic Graphs
Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 169-172

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In this paper we determine necessary and sufficient conditions for the square of a vertex-unicyclic graph to be Hamiltonian. The conditions are simple and easily checked. Further, we show that the square of a vertex-unicyclic graph is Hamiltonian if and only if it is vertex-pancyclic. 
Fleischner, Herbert; Hobbs, Arthur M. Hamiltonian Cycles in Squares of Vertex-Unicyclic Graphs. Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 169-172. doi: 10.4153/CMB-1976-025-3
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     title = {Hamiltonian {Cycles} in {Squares} of {Vertex-Unicyclic} {Graphs}},
     journal = {Canadian mathematical bulletin},
     pages = {169--172},
     year = {1976},
     volume = {19},
     number = {2},
     doi = {10.4153/CMB-1976-025-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-025-3/}
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