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    Bounds For Spectral Radius and Energy of PIS Graphs
    (2024) Öztürk Sözen, Esra; Eryaşar, Elif
    Once the spectral radius and energy of a graph structure have been defined, many properties have been studied. The spectral radius and energy of a graph are related to the eigenvalues of the adjacency matrix of the graph. In this paper, we define an adjacency matrix for a prime ideal sum (PIS) graph and then extend the concepts of spectral radius and energy to PIS graphs. Some bound theorems on the energy and spectral radius of PIS graph structures are given. A SageMath code for plotting these graphs is also provided.
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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)
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    New Formulas and New Bounds for the First and Second Zagreb Indices of Phenylenes
    (2024) Eryaşar, Elif; Sözen, Esra Öztürk; Büyükköse, Şerife
    Graph theory is widely used to represent and analyze chemical structures. In addition, topological indices developed for graphs have a connection with the relationships of chemical structures such as physicochemical and bioactivity. Topological indices are widely used in QSPR-QSAR analysis and have found many applications in chemical graph theory. The oldest known degree-dependent topological indices are the first and second Zagreb indices. These indices have found wide application in chemical structures. Phenylenes containing aromatic and antiaromatic rings exhibit unique physicochemical properties and there is a wide variety of studies on phenylenes. In this article, we present some new formulas and lower bounds for the first and second Zagreb indices molecular structures of phenylenes. In addition, the BFS algorithm method, which is one of the graph algorithms, was used for the first time for the boundary study of chemical structures.
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    On ss-Lifting Modules In View of Singularity
    (2023) Öztürk Sözen, Esra; Eryaşar, Elif
    In this essay we describe δss-lifting modules as a singular version of ss-lifting ones. The focus of this study is to get a more general algebraic structure than ss-lifting modules. A module W is entitled δss-lifting if for each S ≤ W, there occurs a decomposition W = X ⊕ Y with X ≤ S and S ∩ Y ≤ Socδ(Y ), where Socδ(Y ) = δ(Y ) ∩ Soc(Y ). We examine the fundamental properties of this form of modules and also investigate a structure of a ring whose modules are all δss-lifting. Finally, we give several characterizations for (projective) δss-lifting modules and (amply) δss-supplemented modules via δss-perfect rings.