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    Crown Graph

    Definition

    The n-crown graph for an integer n>=3 is the graph with vertex set {x_0, x_1, ..., x_(n - 1), y_0, y_1, ..., y_(n - 1)} and edge set {(x_i, y_j):0<=i, j<=n - 1, i!=j}. It is therefore equivalent to the complete bipartite graph K_(n, n) with "horizontal" edges removed. More formally, the n-crown graph is equivalent to K_(n, n) minus a perfect matching (cf. Brouwer and Koolen 1999, van Dam and Haemers 2003). Note that the term "crown graph" has also been used to refer to a sunlet graph C_n ⊙K_1.