This work defines chain and threshold hypergraphs, highlighting their relationship with connected graphs and spectral radius.
Threshold graphs and chain graphs are the graphs with maximum spectral radius among the family of all connected graphs and connected bipartite graphs, respectively. Several attempts to generalize the concept of threshold graphs to hypergraphs have been carried out. Here we make an attempt to extend the notion of chain graphs to chain hypergraphs and from threshold graphs to threshold hypergraphs. We have characterized the newly defined uniform chain and threshold hypergraphs and have given the simple steps to generate these hypergraphs corresponding to a given binary sequence.
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Shetty et al. (2025) studied this question.
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