A Study on Hub Sets in Hypergraphs - K. S. Shama; P. M. Divya; T. V. Ramakrishnan (International Journal of Mathematics And its Applications, 2025)
The concept of hub sets in hypergraphs, previously introduced in the literature, is further explored in this article. Let \( H \) be a hypergraph. A subset \( S V(H) \) is called a hub set of \( H \) if for every pair of vertices \( u, v V(H) - S \), either \( u \) and \( v \) are adjacent in \( H \), or there exists an \( S \)-hyperpath connecting them. The hub number of \( H \), denoted \( h(H) \), is defined as the minimum cardinality of such a hub set. In this work, the hub number is computed for various classes of hypergraphs. Additionally, the notion of vertex contraction in hypergraphs is introduced, and its influence on the hub number is investigated. Bounds on the hub number in terms of other hypergraph parameters are also established.