Remarks on partially square graphs, hamiltonicity and circumference
Hamamache Kheddouci (2001)
Discussiones Mathematicae Graph Theory
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Given a graph G, its partially square graph G* is a graph obtained by adding an edge (u,v) for each pair u, v of vertices of G at distance 2 whenever the vertices u and v have a common neighbor x satisfying the condition , where . In the case where G is a claw-free graph, G* is equal to G². We define . We give for hamiltonicity and circumference new sufficient conditions depending on σ° and we improve some known results.