For linear bicyclic k-uniform hypergraphs, the maximum Zagreb index is attained by an explicit theta-like hypergraph, and the minimum by any hypergraph with maximum degree 2.
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Extremal Zagreb indices of bicyclic hypergraphs
For linear bicyclic k-uniform hypergraphs, the maximum Zagreb index is attained by an explicit theta-like hypergraph, and the minimum by any hypergraph with maximum degree 2.