Yazar "Oz, Mert Sinan" seçeneğine göre listele
Listeleniyor 1 - 12 / 12
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe A Method for Measuring Similarity or Distance of Molecular and Arbitrary Graphs Based on a Collection of Topological Indices(Wiley, 2025) Oz, Mert SinanThe comparison of graphs using various types of quantitative structural similarity or distance measures has an important place in many scientific disciplines. Two of these are cheminformatics and chemical graph theory, in which the structural similarity or distance measures between molecular graphs are analyzed by calculating the Jaccard/Tanimoto index based on molecular fingerprints. A novel method is proposed to measure the structural similarity or distance for molecular and arbitrary graphs. This method calculates the Jaccard/Tanimoto index based on a collection of topological indices embedded in the entries of a vector. We statistically compare the proposed method with the method for calculating the Jaccard/Tanimoto indices based on five different molecular fingerprints on alkane and cycloalkane isomers. Furthermore, to explore how the method works on non-molecular graphs, we statistically analyze it on the set of all connected graphs with seven vertices. The Jaccard/Tanimoto index values produced by the proposed method cover the value domain. In addition, it provides a discrete similarity distribution with the clustering, which makes the differences clear and provides convenience for comparison. Two outstanding features of the proposed method are its applicability to arbitrary graphs and the computational complexity of the algorithm used in the method is polynomial over the number of graphs and the number of vertices and edges of the graphs.Öğe A survey of the maximal and the minimal nullity in terms of omega invariant on graphs(Sciendo, 2023) Oz, Mert Sinan; Cangul, Ismail NaciLet G = (V, E) be a simple graph with n vertices and m edges. nu(G) and c(G) = m - n + theta be the matching number and cyclomatic number of G, where theta is the number of connected components of G, respectively. Wang and Wong in [18] provided formulae for the upper and the lower bounds of the nullity eta(G) of G as eta(G) = n - 2 nu(G) + 2c(G) and eta(G) = n - 2 nu(G) - c(G), respectively. In this paper, we restate the upper and the lower bounds of nullity eta(G) of G utilizing omega invariant and inherently vertex degrees of G. Also, in the case of the maximal and the minimal nullity conditions are satisfied for G, we present both two main inequalities and many inequalities in terms of Omega invariant, analogously cyclomatic number, number of connected components and vertex degrees of G.Öğe Coefficients of Randic and Sombor characteristic polynomials of some graph types(Ankara Üniversitesi, 2022) Oz, Mert SinanLet GG be a graph. The energy of GG is defined as the summation of absolute values of the eigenvalues of the adjacency matrix of GG. It is possible to study several types of graph energy originating from defining various adjacency matrices defined by correspondingly different types of graph invariants. The first step is computing the characteristic polynomial of the defined adjacency matrix of GG for obtaining the corresponding energy of GG. In this paper, formulae for the coefficients of the characteristic polynomials of both the Randic and the Sombor adjacency matrices of path graph PnPn , cycle graph CnCn are presented. Moreover, we obtain the five coefficients of the characteristic polynomials of both Randic and Sombor adjacency matrices of a special type of 3?regular graph RnRn.Öğe Complementary Topological Indices(Univ Kragujevac, Fac Science, 2025) Furtula, Boris; Oz, Mert SinanAn edge of a graph can be geometrically represented by points (dr, ds) and (ds, dr) in a 2D coordinate system, where coordinates are, obviously, the degrees of the edge's end-vertices. Recently, using such a geometrical point of view of a graph edge, a couple of topological invariants were put forward. They have attracted considerable attention among chemical graph theorists. This paper introduces a novel approach for devising geometrical topological indices. Finally, special attention is focused on the complementary second Zagreb index as a representative of the introduced approach.Öğe Computation method of the Hosoya index of primitive coronoid systems(Amer Inst Mathematical Sciences-Aims, 2022) Oz, Mert Sinan; Cruz, Roberto; Rada, JuanCoronoid systems are natural graph representations of coronoid hydrocarbons associated with benzenoid systems, but they differ in that they contain a hole. The Hosoya index of a graph G is defined as the total number of independent edge sets, that are called k-matchings in G. The Hosoya index is a significant molecular descriptor that has an important position in QSAR and QSPR studies. Therefore, the computation of the Hosoya index of various molecular graphs is needed for making progress on investigations. In this paper, a method based on the transfer matrix technique and the Hosoya vector for computing the Hosoya index of arbitrary primitive coronoid systems is presented. Moreover, the presented method is customized for hollow hexagons by using six parameters. As a result, the Hosoya indices of both each arbitrary primitive coronoid system and also each hollow hexagon can be computed by means of a summation of four selected multiplications consisting of presented transfer matrices and two vectors.Öğe Computing the Number of k-Matchings in Benzenoid Chains(Univ Kragujevac, Fac Science, 2022) Oz, Mert Sinan; Cangul, Ismail NaciThe Hosoya index is associated with many thermodynamic properties such as boiling point, entropy, total pi-electron energy. Transfer matrix technique is extensively utilized in mathematical chemistry for various enumeration problems. In this paper, we introduce the k-matching vector at a certain edge of graph G. Then by using the k-matching vector and two recurrence formulas, we get reduction formulas to compute k-matching number p(G, k) of any benzenoid chains for for all k >= 0 whose summation gives the Hosoya index of the chain. In conclusion, we compute p(G, k) of any benzenoid chains via an appropriate multiplication of three 4(k+ 1) x4(k+ 1) dimensional transfer matrices and a terminal vector which can be obtained by given two algorithms.Öğe Computing the Number of Matchings in Catacondensed Benzenoid Systems(Univ Kragujevac, Fac Science, 2023) Oz, Mert SinanThe Hosoya index of G is defined as the total number of independent edge sets (number of k -matchings p(G; k)) in G. The Hosoya index is one of the most important topological indices in the field of mathematical chemistry because of its relationship with several thermodynamic properties. Therefore, computation of the number of k-matchings of various molecular structures has importance. Two methods, one for computing the number of the Hosoya index of catacondensed benzenoid systems and the other for the number of k-matchings in benzenoid chains (unbranched catacondensed benzenoid systems), have been presented so far. In this paper, a method based on some transfer matrices to compute the number of k -matchings of arbitrary (both unbranched and branched) catacondensed benzenoid systems is presented. Moreover, some algorithms are designed to keep the applicability of the method the same as k increases.Öğe Enumeration of Independent Sets in Benzenoid Chains(Univ Kragujevac, Fac Science, 2022) Oz, Mert Sinan; Cangul, Ismail NaciThe Merrifield-Simmons index of a graph G is defined as the summation of the number i(G, k) of k-independent sets in G. It has applications in structural chemistry such as correlation with the thermodynamic properties of hydrocarbons. For this reason, enumeration of i(G, k) of molecular graphs comes into prominence. In this paper, a method based on the transfer matrix technique is presented for enumerating i(G, k) in benzenoid chains. As a consequence, for all k >= 0, each i(G, k) in arbitrary benzenoid chains is obtained via an appropriate product of three transfer matrices with dimension 5(k + 1) x 5(k + 1) and a vector. In addition, we present two algorithms to make easier application of the method so that the applicability remains the same when the k value increases.Öğe Geometric approach to vertex-degree-based topological indices-Elliptic Sombor index, theory and application(Wiley, 2024) Gutman, Ivan; Furtula, Boris; Oz, Mert SinanA novel geometric method is proposed for constructing vertex-degree-based molecular structure descriptors (topological indices). The model is based on an ellipse whose focal points represent the degrees of a pair of adjacent vertices. This approach enables a geometric interpretation of several previously known topological indices, and lead to design of a few new. The area of the ellipse induces a vertex-degree-based topological index of remarkable simplicity, which we call elliptic Sombor index(ESO$$ ESO $$). The main mathematical properties of ESO$$ ESO $$ are established, especially its relations to other, earlier known, indices. Then the applicative potential of ESO$$ ESO $$ is analyzed. The elliptic Sombor index (ESO) is a topological molecular descriptor derived from the geometric properties of an ellipse. It is defined by using the equation of the area of an ellipse. imageÖğe Geometric-Quadratic Index from a Mathematical Perspective(Univ Kashan, Fac Mathematical Sciences, 2025) Furtula, Boris; Oz, Mert SinanThe geometric-quadratic index (GQ) was defined in 2021 by V. R. Kulli. In a recent study, QSPR analysis for the octane isomers of GQ and some other newly defined topological indices was presented. This analysis has revealed that GQ dominates over many of the well-known topological indices in terms of chemical applicability potential, especially for the heat of vaporization. These results inspired us to investigate the mathematical properties of GQ. In this paper, extremal graphs for GQ are investigated among connected graphs, trees, and unicyclic graphs. In addition, several mathematical relations between GQ and some well-known topological indices are presented. (c) 2025 University of Kashan Press. All rights reserved.Öğe More geometric studies of vertex-degree-based graph indices-tangent Somb or index(Hacettepe Univ, Fac Sci, 2025) Oz, Mert Sinan; Gutman, IvanThe representation of an edge of a graph in a 2-dimensional coordinate system (shown in Fig. 1) made it possible to get a geometric interpretation of several earlier proposed vertex-degree-based graph indices. In particular, the sum of sine, cosine, and secant of the angle alpha (shown in Fig. 1) over all edges of the underlying graph yields, respectively, the second Somb or, inverse symmetric division deg, and symmetric division deg indices. Analogous trigonometric relations for the cosecant and cotangent of alpha are not possible. Therefore, the only remaining such relation is for the tangent of alpha, resulting in a new vertex-degree-based topological index, the tangent Sombor index, Tan. In this paper, the basic properties of Tan are established. Connected graphs and trees reaching extremal Tan-values are characterized. Inequalities between Tan and other graph indices are established. The chemical usefulness of Tan in terms of structure sensitivity, abruptness, degeneracy, and correlation with some physicochemical properties of octane isomers and other indices is investigated.Öğe On properties of the first inverse Nirmala index(Springer, 2025) Furtula, Boris; Oz, Mert SinanThe first inverse Nirmala index is a novel degree-based topological descriptor that was introduced in 2021. Preliminary QSPR investigations suggest that this index deserves further consideration because of its unusually good predictive potential. This paper investigates the relations between this index with some elementary graph quantities and some related degree-based topological index. Further, the computational analysis will reveal extremal graphs among trees, molecular trees, all connected graphs, and their molecular counterparts.
