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    Computing degree based topological indices of algebraic hypergraphs
    (Cell Press, 2024) Alali, Amal S.; Sozen, Esra Ozturk; Abdioglu, Cihat; Ali, Shakir; Eryasar, Elif
    Topological indices are numerical parameters that indicate the topology of graphs or hypergraphs. A hypergraph H = (V (H), E(H)) consists of a vertex set V (H) and an edge set E(H), where each edge e is an element of E(H) is a subset of V(H) with at least two elements. In this paper, our main aim is to introduce a general hypergraph structure for the prime ideal sum (PIS)- graph of a commutative ring. The prime ideal sum hypergraph of a ring R is a hypergraph whose vertices are all non-trivial ideals of R and a subset of vertices E, with at least two elements is a hyperedge whenever I + J is a prime ideal of R for each non-trivial ideal I, J in E, and E, is maximal with respect to this property. Moreover, we also compute some degree-based topological indices (first and second Zagreb indices, forgotten topological index, harmonic index, Randic index, Sombor index) for these hypergraphs. In particular, we describe some degree-based topological indices for the newly defined algebraic hypergraph based on prime ideal sum for Z(n) where n = p(alpha), pq, p(2)q, p(2)q(2), pqr, p(3)q, p(2)qr, pqrs for the distinct primes p, q, r and s.
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    Corrigendum to “Computing degree based topological indices of algebraic hypergraphs” [Heliyon Volume 10, Issue 15, August 2024, e34696] (Heliyon (2024) 10(15), (S240584402410727X), (10.1016/j.heliyon.2024.e34696))
    (Elsevier Ltd, 2025) Alali, Amal S.; Sözen, Esra Öztürk; Abdioğlu, Cihat; Ali, Shakir; Eryaşar, Elif
    In the original published version of this article, there are a few minor figurative and numerical updates: 1. In the proof of Theorem 6, we would like to update the hyperedge to {u1, u4, u5} instead of {u4, u5}. This change affects Figure 2 and 5 (only for Z24).2. In the proof of Theorem 7, hyperedge E3 is extraneous.3. In the proof of Theorem 8, we want to update the degree to d(u10) = 6 instead of d(u10) = 5.As a result of these changes, the numerical values of the topological indices must also be updated. In the published version: Theorem 6: Let [Formula presented]. Then, [Formula presented] [Formula presented] Proof: Let us consider the ideals [Formula presented] are obtained by vertex partition technique. Hence, we get [Formula presented] [Formula presented] [Formula presented] [Formula presented]-Graph and Hypergraph Representations[Figure presented] The authors apologize for the errors. Both the HTML and PDF versions of the article have been updated to correct the errors. © 2025 The Author(s)