On square-Hamiltonian graphs
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
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