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- W2016126876 abstract "The square G 2 of a graph G is the graph having the same vertex set as G and two vertices are adjacent if and only if they are at distance at most 2 from each other. It is known that if G has no cut-vertex, then G 2 is Hamilton-connected (see [G. Chartrand, A.M. Hobbs, H.A. Jung, S.F. Kapoor, C.St.J.A. Nash-Williams, The square of a block is hamiltonian connected, J. Combin. Theory Ser. B 16 (1974) 290–292; R.J. Faudree and R.H. Schelp, The square of a block is strongly path connected, J. Combin. Theory Ser. B 20 (1976) 47–61]). We prove that if G has only one cut-vertex, then G 2 is Hamilton-connected. In the case that G has only two cut-vertices, we prove that if the block that contains the two cut-vertices is hamiltonian, then G 2 is Hamilton-connected. Further, we characterize all graphs with at most one cycle having Hamilton-connected square." @default.
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- W2016126876 date "2009-07-01" @default.
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- W2016126876 title "On graphs whose square have strong hamiltonian properties" @default.
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- W2016126876 doi "https://doi.org/10.1016/j.disc.2009.02.026" @default.
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