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Regularity of bicyclic graphs and their powers

    https://doi.org/10.1142/S0219498820500577Cited by:3 (Source: Crossref)

    Let I(G) be the edge ideal of a bicyclic graph G with a dumbbell as the base graph. In this paper, we characterize the Castelnuovo–Mumford regularity of I(G) in terms of the induced matching number of G. For the base case of this family of graphs, i.e. dumbbell graphs, we explicitly compute the induced matching number. Moreover, we prove that regI(G)q=2q+regI(G)2, for all q1, when G is a dumbbell graph with a connecting path having no more than two vertices.

    Communicated by T. H. Ha

    AMSC: 13D02, 05C25, 05C38, 05E40

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