| R. Motwani and M. Sudan. Square is NP-complete. Manuscript, September 1991. |
....characterization of the squares of graphs involve the concept of clique which is an NP complete problem in general. Furthermore, note that the characterization given by Mukhopadhyay dealing with some n cliques of G which will have exponentially many candidate cliques. Indeed, Motwani and Sudan [20] showed that recognizing the general square graphs is an NP complete problem. Fleischner [8] proved that the square of a biconnected graph is always Hamiltonian. Although the Hamiltonian cycle problem is NP complete for general graphs [10] the biconnectivity of a graph can be tested in linear ....
R. Motwani and M. Sudan. Square is NP-complete. Manuscript, September 1991.
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