Browsing by Author "Cangül, İsmail Naci"
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Publication A new method for the sum-edge characteristic polynomials of graphs(Soc Paranaense Matematica, 2022-01-01) Öz, Mert Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-0700-5774; J-3505-2017In 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.Item A new monoid construction under crossed products(Springer, 2013-12) Emin, Ahmet; Ateş, Firat; İkikardeş, Sebahattin; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 57189022403In this paper we define a new monoid construction under crossed products for given monoids. We also present a generating set and a relator set for this product. Finally, we give the necessary and sufficient conditions for the regularity of it.Publication A presentation and some finiteness conditions for a new version of the schiitzenberger product of monoids(Tübitak Bilimsel ve Teknolojik Araştırma Kurumu, 2016-01-01) Karpuz, Eylem Güzel; Ateş, Firat; Cevik, Ahmet Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7111-3462; 0000-0002-0700-5774; ABA-6206-2020In this paper we first define a new version of the Schutzenberger product for any two monoids A and B, and then, by defining a generating and relator set, we present some finite and infinite consequences of the main result. In the final part of this paper, we give necessary and sufficient conditions for this new version to be periodic and locally finite.Item The (a,b)-Zagreb index of some derived networks(Taylor & Francis, 2019) Sarkar, Prosanta; De, Nilanjan; Pal, Anita; Cangül, İsmail Naci; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; 57189022403There is a very wide application of mathematics in communication theory, signal processing and networking. A network is formed by nodes communicating with each other. Graph theory plays a vital role in the area of networking research. A topological index is a numeric quantity obtained from a graph structure which is invariant under graph isomorphism. In this study, we obtained a generalized degree-based topological index, called -Zagreb index of some derived networks such as Sierpinski network, butterfly network, Benes network and mesh-derived network and hence consider some particular cases.Publication Algebraic structure of graph operations in terms of degree sequences(Etamaths Publ, 2018-01-01) Mishra, Vishnu Narayan; Delen, Sadık; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; J-3505-2017In this paper, by means of the degree sequences (DS) of graphs and some graph theoretical and combinatorial methods, we determine the algebraic structure of the set of simple connected graphs according to two graph operations, namely join and Corona product. We shall conclude that in the case of join product, the set of graphs forms an abelian monoid whereas in the case of Corona product, this set is not even associative, it only satisfies two conditions, closeness and identity element. We also give a result on distributive law related to these two operations.Publication An explicit formula for the harmonic indices and harmonic polynomials of carbon nanocones CNC k (n)(Analytic Publ Co, 2020-01-01) Sardar, Muhammad Shoaib; Xu, Si-Ao; Sajjad, Wasim; Zafar, Sohail; Cangül, İsmail Naci; Farahani, Mohammad R.; CANGÜL, İSMAİL NACİ; 0000-0002-0700-5774; J-3505-2017Let G be a simple molecular graph without directed and multiple edges and without loops. The vertex and edge-sets of G are denoted by V(G) and E(G), respectively. Suppose G is also a connected molecular graph and let u, v is an element of V(G) be two vertices. The harmonic index H(G) of G is defined as the sum of the weights 2(d(u)+d(v))(-1) of all edges in E(G), where d(v) is the degree of a vertex v in G which is defined as the number of vertices of G adjacent to v. The harmonic polynomial of G is defined as H(G, x) = Sigma(e=uv is an element of E(G)) 2x((du+dv-1)) and there is the following nice relation between these two notions H(G) = integral(1)(0) H(G, x)dx. In this paper, we present an explicit formula for the harmonic indices and harmonic polynomials of carbon nanocones CNCk[n].Item Applications of hecke operator to generalized dedekind eta functions(Amer Inst Pyhsics, 2009) Açıkgöz, Mehmet; Kim, Daeyeoul; Şimşek, Yılmaz; Simos, T. E.; Psihoyios, G.; Tsitouras, C.; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; J-3505-2017; 57189022403The aim of this paper is to give relations between generalized Dedekind eta functions, theta functions, Dedekind sums, Hardy-Berndt sums and Hecke operators.Item Bernoulli sayıları, polinomları ve özellikleri(Uludağ Üniversitesi, 2009) Çapkın, Müge; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı.Bu tezde Bernoulli sayıları ve polinomları tanımlanmış ve çeşitli özellikleri ele alınarak, kullanım alanları gösterilmiştir.Bu tez dört bölümden oluşmaktadır. Birinci bölümde çalışmanın diğer bölümlerine temel oluşturacak kavramlar ve teoremler verilmiştir.İkinci bölümde Bernoulli sayıları ve polinomları tanımlanmış ve bunları hesaplamaya yarayan bağıntılar ele alınmıştır. Ayrıca Bernoulli sayıları ve polinomlarının bazı özellikleri ile bu sayılar ve polinomlar arasındaki ilişki gösterilmiştir.Üçüncü bölümde Bernoulli sayıları ve polinomlarının özellikleri verilmeye devam edilmiş, bu sayıların ve polinomların kullanım alanları, benzeri sayılarla olan ilişkileri ve bu sayılar yardımıyla bazı fonksiyonların seri açılımları ele alınmıştır.Dördüncü bölümde ise Bernoulli sayıları ve polinomlarının özel birer halleri olan genelleştirilmiş Bernoulli sayıları ve genelleştirilmiş Bernoulli polinomları tanımlanmış ve bazı özellikleri verilmiştir.Item Bernstein polinomlarının uygulamaları(Uludağ Üniversitesi, 2011) Çetin, Elif; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı.Bu çalışmada Bernstein polinomları tanımlanmış ve önceden verilmiş olan çeşitli özellikleri kullanılarak, Bernstein polinomları ile ilgili yeni sonuçlar bulunmuştur. Bu tez dört bölümden oluşmaktadır. Birinci bölümde çalışmanın diğer bölümlerine temel oluşturacak kavramlar ve teoremler verilmiştir. Ayrıca Gama ve Beta fonksiyonları tanımlanmış ve bu fonksiyonlarla ilgili temel özellikler verilmiştir. İkinci bölümde Bernstein polinomları tanımlanmış ve Bernstein polinomları ile ilgili temel özellikler verilmiştir. Üçüncü bölümde önce Bernstein polinomlarının belirli integralleri incelenmiş ve daha sonra Bernstein polinomlarının çarpımlarının belirli integrallerine yer verilmiştir. Ayrıca Bernstein polinomlarının Gama ve Beta fonksiyonlarıyla olan ilişkisi verilmiştir. Çalışmanın son bölümü olan dördüncü bölümde Bernstein polinomlarının türevleriyle ilgili temel bir sonuçtan yola çıkılarak, öncelikle Bernstein polinomlarının türevlerinin genellemesi verilmiştir. Daha sonra üçüncü bölümdeki Bernstein polinomlarının belirli integralleri ve Bernstein polinomlarının çarpımlarının belirli integrallerinden esinlenerek, Bernstein polinomlarının çarpımlarının türevleri ile ilgili yeni sonuçlar elde edilmiştir.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.Item Calculation of the minimal polynomial of 2cos(π/n) over Q with Maple(American Inst Physics, 2012) Simos, T. E.; Psihoyios, G.; Tsitouras, C.; Anastassi, Z.; Yurttaş, Aysun; Özgür, Birsen; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; ABI-4127-2020; J-3505-2017; AAG-8470-2021; 37090056000; 54403501400; 57189022403The number lambda(q) = 2cos pi/q, q is an element of N, q >= 3, appears in the study of Hecke groups which are Fuchsian groups and in the study of regular polyhedra. There are many results about the minimal polynomial of this algebraic number. Here we obtain the minimal polynomial of these numbers over the field of rationals by means of the better known Chebycheff polynomials and the Maple language.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.Item Classification of normal subgroups of Hecke group H6 in terms of parabolic class number(AIP, 2011) Simos, T. E.; Yurttaş, Aysun; Demirci, Musa; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; 0000-0002-0700-5774; AAG-8470-2021; ABA-6206-2020; J-3505-2017; 37090056000; 23566581100; 57189022403In [3], Greenberg showed that n <= 6t(3) so that mu - nt <= 6t(4) for a normal subgroup N of level n and index mu having t parabolic classes in the modular group Gamma. Accola, [1], improved these to n <= 6t(2) always and n <= t(2) if Gamma/N is not abelian. Newman, [5], obtained another generalisation of these results. Hecke groups are generalisations of the modular group. We particularly deal with one of the most important cases, q = 6.Item Commutator subgroups of the extended Hecke groups (H)over-bar(lambda(q))(Springer Heidelberg, 2004) Şahin, Recep; Bizim, Osman; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; AAH-1468-2021; J-3505-2017; ABA-6206-2020; 9245697900; 57189022403Hecke groups H(lambda(q)) are the discrete subgroups of PSL(2, R) generated by S(z) = -(z + lambda(q))(-1) and T(z) = -1/z. The commutator subgroup of H(lambda(q)), denoted by H'(lambda(q)), is studied in [2]. It was shown that H'(lambda(q)) is a free group of rank q - 1. Here the extended Hecke groups (H) over bar(lambda(q)), obtained by adjoining R-1(z) = 1/(z) over bar to the generators of H(lambda(q)), are considered. The commutator subgroup of (H) over bar(lambda(q)) is shown to be a free product of two finite cyclic groups. Also it is interesting to note that while in the H(lambda(q)) case, the index of H'(lambda(q)) is changed by q, in the case of (H) over bar(lambda(q)), this number is either 4 for q odd or 8 for q even.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 Computing the Merrifield-Simmons indices of benzenoid chains and double benzenoid chains(Springer Heidelberg, 2022-10) Öz, Mert Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-0700-5774; J-3505-2017In this paper, we introduce the Merrifield-Simmons vector defined at a path of corresponding double hexagonal (benzenoid) chain. By utilizing this vector, we present reduction formulae to compute the Merrifield-Simmons index sigma(H) of the corresponding double hexagonal (benzenoid) chain H. As the result, we compute sigma(H) of H by means of a product of some of obtained six matrices and a vector with entries in N. Subsequently, we introduce the simple Merrifield-Simmons vector defined at an edge of given graph G. By using simple Merrifield-Simmons vector we present reduction formulae to compute the sigma(G) where G represents any hexagonal (benzenoid) chain.Item Connectedness criteria for graphs by means of omega invariant(University of Nis, 2020) Şanlı, Utkum; Çelik, Feriha; Delen, Sadık; Cangül, İsmail Naci; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-0700-5774; DRP-0895-2022; CHX-3468-2022; EUU-3205-2022; J-3505-2017; 57194859232; 57202919023; 57204472528; 57189022403A realizable degree sequence can be realized in many ways as a graph. There are several tests for determining realizability of a degree sequence. Up to now, not much was known about the common properties of these realizations. Euler characteristic is a well-known characteristic of graphs and their underlying surfaces. It is used to determine several combinatorial properties of a surface and of all graphs embedded onto it. Recently, last two authors defined a number Ω which is invariant for all realizations of a given degree sequence. Ω is shown to be related to Euler characteristic and cyclomatic number. Several properties of Ω are obtained and some applications in extremal graph theory are done by authors. As already shown, the number Ω gives direct information compared with the Euler characteristic on the realizability, number of realizations, being acyclic or cyclic, number of components, chords, loops, pendant edges, faces, bridges etc. In this paper, another important topological property of graphs which is connectedness is studied by means of Ω. It is shown that all graphs with Ω(G) ≤ −4 are disconnected, and if Ω(G) ≥ −2, then the graph could be connected or disconnected. It is also shown that if the realization is a connected graph and Ω(G) = −2, then certainly the graph should be acyclic. Similarly, it is shown that if the realization is a connected graph G and Ω(G) ≥ 0, then certainly the graph should be cyclic. Also, the fact that when Ω(G) ≤ −4, the components of the disconnected graph could not all be cyclic, and that if all the components of a graph G are cyclic, then Ω(G) ≥ 0 are proven.Item The connections between continued fraction representations of units and certain hecke groups(Malaysian Mathematical Sciences Soc, 2010) Şahin, Recep; İkikardeş, Sebahattin; Koruoğlu, Özden; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; 57189022403Let lambda = root D where D is a square free integer such that D = m(2)+1 for m = 1,3, 4, 5,..., or D = n(2) - 1 form = 2, 3, 4, 5,.... Also, let H(lambda) be the Hecke group associated to A. In this paper, we show that the units in H(lambda) are infinite pure periodic lambda-continued fraction for a certain set of integer D, and hence can not be cusp points.Item The constant term of the minimal polynomial of cos(2 pi/n) over Q(Springer International Publishing, 2013-03) Demirci, Musa; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; 23566581100; 57189022403Let H(lambda(q)) be the Hecke group associated to lambda(q) = 2cos pi/q for q >= 3 integer. In this paper, we determine the constant term of the minimal polynomial of lambda(q) denoted by P-q*(x).Item Determination of genus of normal subgroups of discrete groups(Amer Inst Physics, 2010) Karpuz, Eylem Güzel; Ateş, Fırat; Psihoyios, G.; Tsitouras, C.; Cangül, İsmail Naci; Demirci, Musa; Yurttaş, Aysun; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; AAG-8470-2021; J-3505-2017; 57189022403; 23566581100; 37090056000In this work, subgroups of a special class of discrete subgroups of PLS(2, R), namely the ones of the first kind with genus 0, have been studied. We establish a technique to compute the genus of these subgroups in terms of the genus of easier groups. The method established here can be used for triangle groups, surface groups and Hecke groups (including the well-known modular group).