Person: CANGÜL, İSMAİL NACİ
Loading...
Email Address
Birth Date
Research Projects
Organizational Units
Job Title
Last Name
CANGÜL
First Name
İSMAİL NACİ
Name
57 results
Search Results
Now showing 1 - 10 of 57
Publication Sum-edge characteristic polynomials of graphs(Taylor & Francis, 2019-01-01) Öz, Mert Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Yamaç, Çilem; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; ABA-6206-2020Modelling 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.Publication Inverse problem for albertson irregularity index(Turkic World Mathematical Soc, 2022-01-01) Güneş, Aysun; YURTTAŞ GÜNEŞ, AYSUN; Togan, M.; Demirci, Musa; DEMİRCİ, MUSA; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5349-3978; 0000-0002-0700-5774; A-6557-2018; AAG-8470-2021; J-3505-2017Graph indices have attracted great interest as they give us numerical clues for several properties of molecules. Some indices give valuable information on the molecules under consideration using mathematical calculations only. For these reasons, the calculation and properties of graph indices have been in the center of research. Naturally, the values taken by a graph index is an important problem called the inverse problem. It requires knowledge about the existence of a graph having index equal to a given number. The inverse problem is studied here for Albertson irregularity index as a part of investigation on irregularity indices. A class of graphs is constructed to show that the Albertson index takes all positive even integers. It has been proven that there exists at least one tree with Albertson index equal to every even positive integer but 4. The existence of a unicyclic graph with irregularity index equal to m is shown for every even positive integer m except 4. It is also shown that the Albertson index of a cyclic graph can attain any even positive integer.Publication A constructive method for the cycloidal normal free subgroups of finite index of hecke groups H (√2) AND H (√3)(Acad Sinica, 2006-09-01) DOĞAN, SETENAY; DEMİRCİ, MUSA; Demirci, Musa; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bizim, Osman; BİZİM, OSMAN; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; A-6557-2018; AAH-1468-2021; AAH-9762-2021; J-3505-2017; ABA-6206-2020Cycloidal subgrups of the modular group are studied in [8]. Here cycloidal free normal subgroups of Hecke groups are considered. It is found that when q equivalent to 2 ( mod 4), H ( lambda(q)) has no such subgroups. In all other cases the signatures of these subgroups are constructed by means of q-gons and their signatures are given.Publication Computing the hosoya and the merrifield-simmons indices of two special benzenoid systems(Univ Kashan, Fac Mathematical Sciences, 2021-06-01) Öz, Mert Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; J-3505-2017Gutman et al. gave some relations for computing the Hosoya indices of two special benzenoid systems R-n and P-n. In this paper, we compute the Hosoya index and Merrifield-Simmons index of R-n and P-n, 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 R-n and P-n, by means of a product of a certain matrix of degree n and a certain vector.Publication Maximum and minimum degree energies of p -splitting and p -shadow graphs(Turkic World Mathematical Soc, 2022-01-01) Rao, K. S.; Saravanan, K.; Prakasha, K. N.; Cangul, Ismail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; J-3505-2017Let v(i) and v(j) be two vertices of a graph G. The maximum degree matrix of G is given in [2] byd(ij) = {max{d(i), d(j)} if v(i) and v(j) are adjacent0 otherwise.Similarly the (i, j)-th entry of the minimum degree matrix is defined by taking the minimum degree instead of the maximum degree above, [1]. In this paper, we have elucidated a relation between maximum degree energy of p-shadow graphs with the maximum degree energy of its underlying graph. Similarly, a relation has been derived for minimum degree energy also. We disprove the results E-M(S'(G)) = 2E(M)(G) and E-m(S'(G)) = 2E(m)(G) given by Zheng-Qing Chu et al. [3] by giving some counterexamples.Publication Bounds for the sum of cubes of vertex degrees of splice graphs(Turkic World Mathematical, 2020-01-01) Lokesha, Veerebradiah; Jain, Sushmitha; Muddalapuram, Manjunath; Çevik, Ahmet Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017Some chemically interesting graphs can be derived from simpler graphs by some graph operations. One of the most relevant among these interesting graphs is named as splice graphs. They are related to RNA sequencing and therefore is of great interest. The main target of this paper is to obtain the explicit interpretation of F-index in terms of the graph size and maximum or minimum vertex degrees of special splice graphs.Publication Changing relationship between sets using convolution sums of restricted divisor(Korean Soc Computational & Applied Mathematics-kscam, 2023-01-01) Cangül, İsmail Naci; Kim, Daeyeoul; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; J-3505-2017There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one may change their opinion or position rapidly. In this work, we think of the problem of changing relationships from a mathematical point of view and think of an answer. In some sense, we comment these changes as power changes. Our number theoretical model will be based on this idea. Using the convolution sum of the restricted divisor function E, we obtain the answer to this problem.Publication Computing the number of k-matchings in benzenoid chains(Univ Kragujevac, Fac Science, 2022-01-01) Öz, Mert Sinan; Cangül, Ismail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017The 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.Publication Omega index of line and total graphs(Hindawi, 2021-09-09) Demirci, Musa; Delen, Sadık; Çevik, Ahmet Sinan; Cangül, İsmail Naci; DEMİRCİ, MUSA; Delen, Sadık; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-6439-8439; 0000-0003-4689-3660; 0000-0002-0700-5774; A-6557-2018; EUU-3205-2022 ; J-3505-2017A derived graph is a graph obtained from a given graph according to some predetermined rules. Two of the most frequently used derived graphs are the line graph and the total graph. Calculating some properties of a derived graph helps to calculate the same properties of the original graph. For this reason, the relations between a graph and its derived graphs are always welcomed. A recently introduced graph index which also acts as a graph invariant called omega is used to obtain such relations for line and total graphs. As an illustrative exercise, omega values and the number of faces of the line and total graphs of some frequently used graph classes are calculated.Publication Some graph parameters of power set graphs(Pushpa Publishing House, 2021-03-01) Nacaroğlu, Yaşar; Akgüneş, Nihat; Pak, Sedat; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; J-3505-2017In this study, we examine some graph parameters such as the edge number, chromatic number, girth, domination number and clique number of power set graphs.