Yazar "Abdioglu, Cihat" seçeneğine göre listele

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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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    Öğe
    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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    Öğe
    Forgotten Topological and Wiener Indices of Prime Ideal Sum Graph of Zn
    (Bentham Science Publ Ltd, 2024) Sozen, Esra Ozturk; Eryasar, Elif; Abdioglu, Cihat
    Background: Chemical graph theory is a sub-branch of mathematical chemistry, assuming each atom of a molecule is a vertex and each bond between atoms as an edge. Objective: Owing to this theory, it is possible to avoid the difficulties of chemical analysis because many of the chemical properties of molecules can be determined and analyzed via topological indices. Due to these parameters, it is possible to determine the physicochemical properties, biological activities, environmental behaviours and spectral properties of molecules. Nowadays, studies on the zero divisor graph of Z(n) via topological indices is a trending field in spectral graph theory. Methods: For a commutative ring R with identity, the prime ideal sum graph of R is a graph whose vertices are nonzero proper ideals of R and two distinctvertices I and J are adjacent if and only if I+J is a prime ideal of R. Results: In this study the forgotten topological index and Wiener index of the prime ideal sum graph of Z(n) are calculated for n=p(alpha), pq, p(2)q, p(2)q(2), pqr, p(3)q, p(2)qr, pqrs where p,q,r and s are distinct primes and a Sage math code is developed for designing graph and computing the indices. Conclusion: In the light of this study, it is possible to handle the other topological descriptors for computing and developing new algorithms for next studies and to study some spectrum and graph energies of certain finite rings with respect to PIS-graph easily.