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Öğe 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, ElifIn 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)Öğe On the genus and crosscap of the extended sum annihilating-ideal graph of commutative rings(Springer, 2025) Nazim, Mohd; Ur Rehman, Nadeem; Abdioğlu, Cihat; Mir, Shabir Ahmad; NazimIn the context of a commutative ring with unity, denoted as S, and its associated set of annihilating ideals A(S), there exists a graph known as the extended sum annihilating-ideal graph, denoted as AGΩ(S). This graph has its vertex set derived from the set A(S)*, and it exhibits a specific pattern of connections between its vertices. More precisely, two distinct vertices, referred to as ℑ1 and ℑ2, are linked by an edge if and only if one of the following conditions holds: either ℑ1ℑ2=0 or ℑ1 +ℑ2 ∈ A(S). In the following research paper, we delve into the classification of Artinian commutative rings, denoted as S, with a particular focus on those where the extended sum annihilating-ideal graph takes on one of three distinct forms: a double toroidal graph, a projective plane, or a Klein bottle. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.Öğe On soft functionals and soft duality(Amer Inst Physics, 2016) Yazar, Murat İbrahim; Aslan, I.; Bayrak, Y.; Akdemir, A. O.; Ekinci, A.; Polat, K.; Dadasoglu, F; Türkoğlu, E. A.In this study, firstly we define a soft inner product space on soft real numbers and show that this space is a soft normed space. Secondly, we define soft linear functionals on this space and investigate some of its properties. Thirdly, we introduce the soft dual space of this soft normed space. Finally, by using the soft linear operator defined in [10] we state and prove a theorem about the continuity of soft dual operator.
