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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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    Computing Topological Descriptors of Prime Ideal Sum Graphs of Commutative Rings
    (Mdpi, 2023) Ozturk Sozen, Esra; Alsuraiheed, Turki; Abdioglu, Cihat; Ali, Shakir
    Let n >= 1 be a fixed integer. The main objective of this paper is to compute some topological indices and coindices that are related to the graph complement of the prime ideal sum (PIS) graph of Zn, where n=p alpha,p2q,p2q2,pqr,p3q,p2qr, and pqrs for the different prime integers p,q,r, and s. Moreover, we construct M-polynomials and CoM-polynomials using the PIS-graph structure of Zn to avoid the difficulty of computing the descriptors via formulas directly. Furthermore, we present a geometric comparison for representations of each surface obtained by M-polynomials and CoM-polynomials. Finally, we discuss the applicability of algebraic graphs to chemical graph theory.
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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)