Yazar "Cangul, Ismail Naci" seçeneğine göre listele

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    A New Method for the Sum-Edge Characteristic Polynomials of Graphs
    (Boletim da Sociedade Paranaense de Matematica, 2022) Öz, Mert Sinan; Cangul, Ismail Naci
    In this paper, the determinant of the sum-edge adjacency matrix of any given graph without loops is calculated by means of an algebraic method using spanning elementary subgraphs and also the coefficients of the corresponding sum-edge characteristic polynomial are determined by means of the elementary subgraphs. Also, we provide a formula for calculating the number of smallest odd-sized cycles in a given regular graph.
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    A survey of the maximal and the minimal nullity in terms of omega invariant on graphs
    (Sciendo, 2023) Oz, Mert Sinan; Cangul, Ismail Naci
    Let 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.
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    Computing the Hosoya and the Merrifield-Simmons Indices of Two Special Benzenoid Systems
    (University of Kashan, 2021) Öz, Mert Sinan; Cangul, Ismail Naci
    Gutman et al. gave some relations for computing the Hosoya indices of two special benzenoid systems Rn and Pn. In this paper, we compute the Hosoya index and Merrifield-Simmons index of Rn and Pn by means of introducing four vectors for each benzenoid system and index. As a result, we compute the Hosoya index and the Merrifield-Simmons index of Rn and Pn by means of a product of a certain matrix of degree n and a certain vector.
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    Computing the Number of k-Matchings in Benzenoid Chains
    (Univ Kragujevac, Fac Science, 2022) Oz, Mert Sinan; Cangul, Ismail Naci
    The 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.
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    Enumeration of Independent Sets in Benzenoid Chains
    (Univ Kragujevac, Fac Science, 2022) Oz, Mert Sinan; Cangul, Ismail Naci
    The 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.
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    Matching number and characteristic polynomial of a graph
    (Taylor & Francis Ltd, 2020) Yurttas Gunes, Aysun; Demirci, Musa; Öz, Mert Sinan; Cangul, Ismail Naci
    Matching number and the spectral properties depending on the characteristic polynomial of a graph obtained by means of the adjacency polynomial has many interesting applications in different areas of science. There are some work giving the relation of these two areas. Here the relations between these two notions are considered and several general results giving this relations are obtained. A result given for only unicyclic graphs is generalized. There are some methods for determining the matching number of a graph in literature. Usually nullity, spanning trees and several graph parts are used to do this. Here, as a new method, the conditions for calculating the matching number of a graph by means of the coefficients of the characteristic polynomial of the graph are determined. Finally some results on the matching number of graphs are obtained.
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    Sum-edge characteristic polynomials of graphs
    (Taylor & Francis Ltd, 2019) Öz, Mert Sinan; Yamac, Cilem; Cangul, Ismail Naci
    Modelling a chemical compound by a (molecular) graph helps us to obtain some required information about the chemical and physical properties of the corresponding molecular structure. Linear algebraic notions and methods are used to obtain several properties of graphs usually by the help of some graph matrices and these studies form an important sub area of Graph Theory called spectral graph theory. In this paper, we deal with the sum-edge matrices defined by means of vertex degrees. We calculate the sum-edge characteristic polynomials of several important graph classes by means of the corresponding sum-edge matrices.