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Hamiltonicity of double domination critical claw-free graphs

2018
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Discussiones Mathematicae Graph Theory
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A graph G with the double domination number γ ×2 (G) = k is said to be k-γ ×2 -critical if γ ×2 (G + uv) < k for any uv / ∈ E(G). On the other hand, a graph G with γ ×2 (G) = k is said to be k-γ + ×2 -stable if γ ×2 (G + uv) = k for any uv / ∈ E(G) and is said to be k-γ − ×2 -stable if γ ×2 (G − uv) = k for any uv ∈ E(G). The problem of interest is to determine whether or not 2-connected k-γ ×2 -critical graphs are Hamiltonian. In this paper, for k ≥ 4, we provide a 2-connected k-γ ×2 -critical

doi:10.7151/dmgt.2148
fatcat:zcqolhixk5ccdnvhhtg3zrp5dm