Hyper-Zagreb Indices of Hypergraphs with Application in Drug Design
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912590519599104 |
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| author | Sanad, Abdulkafi |
| author_facet | Sanad, Abdulkafi |
| contents | Let $\mathcal{H}$ be a hypergraph on the non-empty finite vertex set $V(\mathcal{H})$ with the hyperedge set $E(\mathcal{H})$, where each hyperedge $e \in E(\mathcal{H})$ is a subset of $V(\mathcal{H})$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13787 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyper-Zagreb Indices of Hypergraphs with Application in Drug Design Sanad, Abdulkafi Discrete Mathematics Let $\mathcal{H}$ be a hypergraph on the non-empty finite vertex set $V(\mathcal{H})$ with the hyperedge set $E(\mathcal{H})$, where each hyperedge $e \in E(\mathcal{H})$ is a subset of $V(\mathcal{H})$ 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. |
| title | Hyper-Zagreb Indices of Hypergraphs with Application in Drug Design |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2509.13787 |