Browsing by Author "Çevik, Ahmet Sinan"
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Item Analysis approach to finite monoids(Springer International Publishing, 2013) Çevik, Ahmet Sinan; Şimşek, Yılmaz; Cangül, Naci İsmail; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; ABA-6206-2020; 57189022403In a previous paper by the authors, a new approach between algebra and analysis has been recently developed. In detail, it has been generally described how one can express some algebraic properties in terms of special generating functions. To continue the study of this approach, in here, we state and prove that the presentation which has the minimal number of generators of the split extension of two finite monogenic monoids has different sets of generating functions (such that the number of these functions is equal to the number of generators) that represent the exponent sums of the generating pictures of this presentation. This study can be thought of as a mixture of pure analysis, topology and geometry within the purposes of this journal.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 Fibonacci graphs(MDPI, 2020-08-14) Çevik, Ahmet Sinan; Güneş, Aysun Yurttaş; Delen, Sadık; Demirci, Musa; Cangül, İsmail Naci; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0003-4689-3660; 0000-0002-6439-8439; J-3505-2017; AAG-8470-2021; 37090056000; 57204472528; 23566581100; 57189022403Apart from its applications in Chemistry, Biology, Physics, Social Sciences, Anthropology, etc., there are close relations between graph theory and other areas of Mathematics. Fibonacci numbers are of utmost interest due to their relation with the golden ratio and also due to many applications in different areas from Biology, Architecture, Anatomy to Finance. In this paper, we define Fibonacci graphs as graphs having degree sequence consisting of n consecutive Fibonacci numbers and use the invariant omega to obtain some more information on these graphs. We give the necessary and sufficient conditions for the realizability of a set D of n successive Fibonacci numbers for every n and also list all possible realizations called Fibonacci graphs for 1 <= n <= 4.Item Generalization for Estrada index(Amer Inst Physics, 2010) Güngör, Ayşe Dilek; Çevik, Ahmet Sinan; Karpuz, Eylem Güzel; Ateş, Fırat; Psihoyios, G.; Tsitouras, C.; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; 57189022403In this paper the Estrada index of Hermite matrix is firstly defined and investigated. In fact this is a natural generalization of Estrada, distance Estrada and Laplacian Estrada indices. Thus all properties about them can be handled by this new index.Item The graph based on Grobner-Shirshov bases of groups(Springer, 2013-03-26) Karpuz, Eylem Güzel; Ateş, Fırat; Çevik, Ahmet Sinan; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; 0000-0002-0700-5774; J-3505-2017; ABA-6206-2020; 57189022403Let us consider groups G(1) = Z(k) * (Z(m) * Z(n)), G(2) = Z(k) x (Z(m) * Z(n)), G(3) = Z(k) * (Z(m) x Z(n)), G(4) = (Z(k) * Z(l)) * (Z(m) * Z(n)) and G(5) = (Z(k) * Z(l)) x (Z(m) * Z(n)), where k, l, m, n = 2. In this paper, by defining a new graph Gamma(G(i)) based on the Grobner-Shirshov bases over groups G(i), where 1 <= i <= 5, we calculate the diameter, maximum and minimum degrees, girth, chromatic number, clique number, domination number, degree sequence and irregularity index of Gamma(G(i)). Since graph theoretical studies (including such above graph parameters) consist of some fixed point techniques, they have been applied in such fields as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory and physics. In addition, the Grobner-Shirshov basis and the presentations of algebraic structures contain a mixture of algebra, topology and geometry within the purposes of this journal.Item Inverse problem for sigma index(University of Kragujevac, 2018) Gutman, Ivan; Çevik, Ahmet Sinan; Togan, Müge; Yurttaş, Aysun; Naci Cangül, İsmail; Uludağ Üniversitesi/Fen - Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; GBL-2333-2022; AAG-8470-2021; J-3505-2017; 54403978300; 37090056000; 57189022403If G is a (molecular) graph and d(v), the degree of its vertex u, then its sigma index is defined as sigma(G) = Sigma(d(u) - d(v))(2), with summation going over all pairs of adjacent vertices. Some basic properties of sigma(G) are established. The inverse problem for topological indices is about the existence of a graph having its index value equal to a given non-negative integer. We study the problem for the sigma index and first show that sigma(G) is an even integer. Then we construct graph classes in which sigma(G) covers all positive even integers. We also study the inverse problem for acyclic, unicyclic, and bicyclic graphs.Item The multiplicative Zagreb indices of graph operations(Springer, 2013) Das, Kinkar C.; Çevik, Ahmet Sinan; Yurttaş, Aysun; Togan, Müge; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; 0000-0002-0700-5774; J-3505-2017; AAG-8470-2021; ABA-6206-2020; 37090056000; 54403978300; 57189022403Recently, Todeschini et al. (Novel Molecular Structure Descriptors - Theory and Applications I, pp. 73-100, 2010), Todeschini and Consonni (MATCH Commun. Math. Comput. Chem. 64:359-372, 2010) have proposed the multiplicative variants of ordinary Zagreb indices, which are defined as follows: Pi(1) = Pi(1)(G) = Pi(v is an element of V(G)) d(G)(V)(2), Pi(2) = Pi(2)(G) = Pi(uv is an element of E(G)) d(G)(u)d(G)(V). These two graph invariants are called multiplicative Zagreb indices by Gutman (Bull. Soc. Math. Banja Luka 18:17-23, 2011). In this paper the upper bounds on the multiplicative Zagreb indices of the join, Cartesian product, corona product, composition and disjunction of graphs are derived and the indices are evaluated for some well-known graphs. MSC: 05C05, 05C90, 05C07.Item A new approach to connect algebra with analysis: Relationships and applications between presentations and generating functions(Springer, 2013-03-14) Şimşek, Yılmaz; Çevik, Ahmet Sinan; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; 57189022403For a minimal group (or monoid) presentation P, let us suppose that P satisfies the algebraic property of either being efficient or inefficient. Then one can investigate whether some generating functions can be applied to it and study what kind of new properties can be obtained by considering special generating functions. To establish that, we will use the presentations of infinite group and monoid examples, namely the split extensions Z(n) X Zand Z(2) X Z, respectively. This study will give an opportunity to make a new classification of infinite groups and monoids by using generating functions.Item New bounds for Randic and GA indices(Springer, 2013) Lokesha, V.; Shetty, B. Shwetha; Ranjini, P. S.; Çevik, Ahmet Sinan; 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; 57189022403The main goal of this paper is to present some new lower and upper bounds for the Randic and GA indices in terms of Zagreb and modified Zagreb indices.Item A new example of deficiency one groups(Amer Inst Physics, 2010) Çevik, Ahmet Sinan; Güngör, Dilek; Karpuz, Eylem Güzel; Ateş, Fırat; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; 57189022403The main purpose of this paper is to present a new example of deficiency one groups by considering the split extension of a finite cyclic group by a free abelian group having rank two.Item New formulae for zagreb indices(Amer Inst Physics, 2017) Simos, T.; Tsitouras, C.; Çevik, Ahmet Sinan; Cangül, İsmail Naci; Yurttaş, Aysun; Togan, Müge; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; AAG-8470-2021; 57189022403; 37090056000; 54403978300In this paper, we study with some graph descriptors also called topological indices. These descriptors are useful in determination of some properties of chemical structures and preferred to some earlier descriptors as they are more practical. Especially the first and second Zagreb indices together with the first and second multiplicative Zagreb indices are considered and they are calculated in terms of the smallest and largest vertex degrees and vertex number for some well-known classes of graphs.Item A new graph based on the semi-direct product of some monoids(Springer, 2013) Karpuz, Eylem Guzel; Das, Kinkar Chandra; Çevik, Ahmet Sinan; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; J-3505-2017; ABA-6206-2020; 57189022403In this paper, firstly, we define a new graph based on the semi-direct product of a free abelian monoid of rank n by a finite cyclic monoid, and then discuss some graph properties on this new graph, namely diameter, maximum and minimum degrees, girth, degree sequence and irregularity index, domination number, chromatic number, clique number of Gamma (P-M). Since graph theoretical studies (including such above graph parameters) consist of some fixed point techniques, they have been applied in fields such as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory and physics.Item The next step of the word problem over monoids(Elsevier Science, 2011-10) Karpuz, Eylem Güzel; Ateş, Fırat; Çevik, Ahmet Sinan; Maden, Ayşe Dilek Güngör; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/MatematikBölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; 57189022403It is known that a group presentation P can be regarded as a 2-complex with a single 0-cell. Thus we can consider a 3-complex with a single 0-cell which is known as a 3-presentation. Similarly, we can also consider 3-presentations for monoids. In this paper, by using spherical monoid pictures, we show that there exists a finite 3-monoid-presentation which has unsolvable "generalized identity problem'' that can be thought as the next step (or one-dimension higher) of the word problem for monoids. We note that the method used in this paper has chemical and physical applications.Item The number of spanning trees of a graph(Springer, 2013-08) Das, Kinkar Chandra; Çevik, Ahmet Sinan; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; 0000-0003-2576-160X; J-3505-2017; 57189022403Let G be a simple connected graph of order n, m edges, maximum degree Delta(1) and minimum degree delta. Li et al. (Appl. Math. Lett. 23: 286-290, 2010) gave an upper bound on number of spanning trees of a graph in terms of n, m, Delta(1) and delta: t(G) <= delta (2m-Delta(1)-delta-1/n-3)(n-3). The equality holds if and only if G congruent to K-1,K-n-1, G congruent to K-n, G congruent to K-1 boolean OR (K-1 boolean OR Kn-2) or G congruent to K-n - e, where e is any edge of K-n. Unfortunately, this upper bound is erroneous. In particular, we show that this upper bound is not true for complete graph K-n. In this paper we obtain some upper bounds on the number of spanning trees of graph G in terms of its structural parameters such as the number of vertices (n), the number of edges (m), maximum degree (Delta(1)), second maximum degree (Delta(2)), minimum degree (delta), independence number (alpha), clique number (omega). Moreover, we give the Nordhaus-Gaddum-type result for number of spanning trees.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.Item On average eccentricity of graphs(Natl Acad Sciences, 2016-10-20) Das, Kinkar Chandra; Maden, Ayşe Dilek; Çevik, Ahmet Sinan; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; 57189022403The eccentricity of a vertex is the maximum distance from it to any other vertex and the average eccentricity avec(G) of a graph G is the mean value of eccentricities of all vertices of G. In this paper we present some lower and upper bounds for the average eccentricity of a connected (molecular) graph in terms of its structural parameters such as number of vertices, diameter, clique number, independence number and the first Zagreb index. Also, we obtain a relation between average eccentricity and first Zagreb index. Moreover, we compare average eccentricity with graph energy, ABC index and index.Item On Sombor Index(MDPI, 2021-02) Das, Kinkar Chandra; Çevik, Ahmet Sinan; Shang, Yilun; Cangül, İsmail Naci; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-0700-5774; J-3505-2017; 57189022403The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO=SO(G)= Sigma(vivj is an element of E(G)) root d(G)(v(i))(2)+d(G)(v(j))(2), where d(G)(v(i)) is the degree of vertex vi in G. Here, we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work.Item On the efficiency of semi-direct products of finite cyclic monoids by one-relator monoids(Amer Inst Physics, 2010) Ateş, Fırat; Karpuz, Eylem Güzel; Güngör, Ayşe Dilek Maden; Çevik, Ahmet Sinan; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; 57189022403In this paper we give necessary and sufficient conditions for the efficiency of a standard presentation for the semi-direct product of finite cyclic monoids by one-relator monoids.Item On the Harary index of graph operations(Springer, 2013) Das, Kinkar C.; Xu, Kexiang; Çevik, Ahmet Sinan; Graovac, Ante; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; 57189022403The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, expressions for the Harary indices of the join, corona product, Cartesian product, composition and disjunction of graphs are derived and the indices for some well-known graphs are evaluated. In derivations some terms appear which are similar to the Harary index and we name them the second and third Harary index.Item On the Kirchhoff matrix, a new Kirchhoff index and the Kirchhoff energy(Springer, 2013) Maden, Ayşe Dilek Güngör; Çevik, Ahmet Sinan; Das, Kinkar Chandra; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; J-3505-2017; 57189022403The main purpose of this paper is to define and investigate the Kirchhoff matrix, a new Kirchhoff index, the Kirchhoff energy and the Kirchhoff Estrada index of a graph. In addition, we establish upper and lower bounds for these new indexes and energy. In the final section, we point out a new possible application area for graphs by considering this new Kirchhoff matrix. Since graph theoretical studies (including graph parameters) consist of some fixed point techniques, they have been applied in the fields such as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory, and physics.