Yazar "Cangul, Ismail Naci" seçeneğine göre listele

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    Inverse Problem for Sigma Index
    (UNIV KRAGUJEVAC, FAC SCIENCE, 2018) Gutman, Ivan; Togan, Muge; Yurttas, Aysun; Cevik, Ahmet Sinan; Cangul, Ismail Naci
    If 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.
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    The multiplicative Zagreb indices of graph operations
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Das, Kinkar C.; Yurttas, Aysun; Togan, Muge; Cevik, Ahmet Sinan; Cangul, Ismail Naci
    Recently, 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.
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    A new approach to connect algebra with analysis: relationships and applications between presentations and generating functions
    (SPRINGEROPEN, 2013) Cangul, Ismail Naci; Cevik, Ahmet Sinan; Simsek, Yilmaz
    For 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.
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    New bounds for Randic and GA indices
    (SPRINGEROPEN, 2013) Lokesha, V.; Shetty, B. Shwetha; Ranjini, P. S.; Cangul, Ismail Naci; Cevik, Ahmet Sinan
    The 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.
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    New Formulae for Zagreb Indices
    (AMER INST PHYSICS, 2017) Cangul, Ismail Naci; Yurttas, Aysun; Togan, Muge; Cevik, Ahmet Sinan
    In 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.
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    A new graph based on the semi-direct product of some monoids
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Karpuz, Eylem Guzel; Das, Kinkar Chandra; Cangul, Ismail Naci; Cevik, Ahmet Sinan
    In 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.
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    On the Harary index of graph operations
    (SPRINGEROPEN, 2013) Das, Kinkar C.; Xu, Kexiang; Cangul, Ismail Naci; Cevik, Ahmet Sinan; Graovac, Ante
    The 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.
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    On the Kirchhoff matrix, a new Kirchhoff index and the Kirchhoff energy
    (SPRINGEROPEN, 2013) Maden, Ayse Dilek; Cevik, Ahmet Sinan; Cangul, Ismail Naci; Das, Kinkar C.
    The 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.
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    On the spectral radius of bipartite graphs which are nearly complete
    (SPRINGEROPEN, 2013) Das, Kinkar Chandra; Cangul, Ismail Naci; Maden, Ayse Dilek; Cevik, Ahmet Sinan
    For p, q, r, s, t is an element of Z(+) with rt <= p and st <= q, let G = G(p, q; r, s; t) be the bipartite graph with partite sets U = {u(1), ..., u(p)} and V = {v(1),..., v(q)} such that any two edges u(i) and v(j) are not adjacent if and only if there exists a positive integer k with 1 <= k <= t such that (k - 1) r + 1 <= i <= kr and (k - 1) s + 1 <= j <= ks. Under these circumstances, Chen et al. (Linear Algebra Appl. 432: 606-614, 2010) presented the following conjecture: Assume that p <= q, k < p, vertical bar U vertical bar = p, vertical bar V vertical bar = q and vertical bar E(G)vertical bar = pq - k. Then whether it is true that lambda(1)(G) <= lambda(1)(G(p, q; k, 1; 1)) = root pq - k + root p(2)q(2) - 6pqk + 4pk + 4qk(2) - 3k(2)/2. In this paper, we prove this conjecture for the range min(vh is an element of V){deg v(h)} <= left perpendicular p-1/2right perpendicular.
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    A presentation and some finiteness conditions for a new version of the Schiitzenberger product of monoids
    (SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2016) Karpuz, Eylem Guzel; Ates, Firat; Cevik, Ahmet Sinan; Cangul, Ismail Naci
    In 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.
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    Some array polynomials over special monoid presentations
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Cevik, Ahmet Sinan; Das, Kinkar Chandra; Simsek, Yilmaz; Cangul, Ismail Naci
    In a recent joint paper (Cevik et al. in Hacet. J. Math. Stat., acceptted), the authors have investigated the p-Cockcroft property (or, equivalently, efficiency) for a presentation, say , of the semi-direct product of a free abelian monoid rank two by a finite cyclic monoid. Moreover, they have presented sufficient conditions on a special case for to be minimal whilst it is inefficient. In this paper, by considering these results, we first show that the presentations of the form can actually be represented by characteristic polynomials. After that, some connections between representative characteristic polynomials and generating functions in terms of array polynomials over the presentation will be pointed out. Through indicated connections, the existence of an equivalence among each generating function in itself is claimed studied in this paper. MSC: 11B68, 11S40, 12D10, 20M05, 20M50, 26C05, 26C10.
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    Some fixed-point results on (generalized) Bruck-Reilly *-extensions of monoids
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Karpuz, Eylem Guzel; Cevik, Ahmet Sinan; Koppitz, Joerg; Cangul, Ismail Naci
    In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly *-extensions of arbitrary monoids to be regular, coregular and strongly pi-inverse. These semigroup classes have applications in various field of mathematics, such as matrix theory, discrete mathematics and p-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal.