Browsing by Author "Deniz, Zakir"

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    On the well-coveredness of square graphs
    (Ankara Üniversitesi, 2022) Deniz, Zakir; Other; Other
    The square of a graph G is obtained from G by putting an edge between two distinct vertices whenever their distance in G is 2. A graph is well-covered if every maximal independent set in the graph is of the same size. In this paper, we investigate the graphs whose squares are well-covered. We first provide a characterization of the trees whose squares are well-covered. Afterwards, we show that a bipartite graph G and its square are well-covered if and only if every component of G is K 1 or K r , r for some r ≥ 1 . Moreover, we obtain a characterization of the graphs whose squares are well-covered in the case α ( G ) = α ( G 2 ) + k for k ∈ { 0 , 1 } .