2025/09/17 by Abdulkafi Sanad, Sanad, Abdulkafi
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Computational Drug Discovery Methods #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2509.13787
openalex publication_date 2025/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H be a hypergraph on the non-empty finite vertex set V(H) with the hyperedge set E(H), where each hyperedge e ∈ E(H) is a subset of V(H) with at least two vertices. This paper introduces the first and second Hyper-Zagreb indices for hypergraphs, extending these well-known graph indices to hypergraphs. We discuss bounds on these indices for general hypergraphs, weak bipartite hypergraphs, hypertrees, k-uniform hypergraphs, k-uniform weak bipartite hypergraphs, and k-uniform hypertrees, characterizing the extremal hypergraphs that achieve these bounds. Additionally, we present a novel application of these indices in drug design and bioactivity prediction, demonstrating their utility in quantitative structure-activity relationship (QSAR) modeling.