Yazar "Çevik, A. Sinan" seçeneğine göre listele

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    Grobner-Shirshov Bases of the Generalized Bruck-Reilly *-Extension
    (WORLD SCIENTIFIC PUBL CO PTE LTD, 2012) Kocapınar, Canan; Karpuz, Eylem Güzel; Ateş, Fırat; Çevik, A. Sinan
    In this paper we first define a presentation for the generalized Bruck-Reilly *-extension of a monoid and then we work on its Grobner-Shirshov bases.
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    A new bound of radius with irregularity index
    (ELSEVIER SCIENCE INC, 2013) Akgüneş, Nihat; Çevik, A. Sinan
    In this paper, we use a technique introduced in the paper [P. Dankelmann, R. C. Entringer, Average distance, minimum degree and spanning trees, J. Graph Theory 33 (2000), 1-13] to obtain a strengthening of an old classical theorem by Erdos et al. [P. Erdos, J. Pach, R. Pollack, Z. Tuza, Radius, diameter, and minimum degree, J. Combin. Theory B 47 (1989), 73-79] on radius and minimum degree. To be more detailed, we will prove that if G is a connected graph of order n with the minimum degree delta, then the radius G does not exceed 3/2(n - t + 1/delta + 1 + 1) where t is the irregularity index (that is the number of distinct terms of the degree sequence of G) which has been recently defined in the paper [S. Mukwembi, A note on diameter and the degree sequence of a graph, Appl. Math. Lett. 25 (2012), 175-178]. We claim that our result represent the tightest bound that ever been obtained until now. (C) 2012 Elsevier Inc. All rights reserved.
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    A New Example of Deficiency One Groups
    (Amer Inst Physics, 2010) Çevik, A. Sinan; Güngör, A. Dilek; Karpuz, Eylem G.; Ateş, Fırat; Cangül, I. Naci
    The 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.
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    On a graph of monogenic semigroups
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Das, Kinkar Ch.; Akgüneş, Nihat; Çevik, A. Sinan
    Let us consider the finite monogenic semigroup S-M with zero having elements {x, x(2), x(3), ... , x(n)}. There exists an undirected graph Gamma (S-M) associated with S-M whose vertices are the non-zero elements x, x(2), x(3), ... , x(n) and, f or 1 <= i, j <= n, any two distinct vertices xi and xj are adjacent if i + j > n. In this paper, the diameter, girth, maximum and minimum degrees, domination number, chromatic number, clique number, degree sequence, irregularity index and also perfectness of Gamma (S-M) have been established. In fact, some of the results obtained in this section are sharper and stricter than the results presented in DeMeyer et al. (Semigroup Forum 65:206-214, 2002). Moreover, the number of triangles for this special graph has been calculated. In the final part of the paper, by considering two (not necessarily different) graphs Gamma (S-M(1)) and Gamma (S-M(2)), we present the spectral properties to the Cartesian product Gamma (S-M(1)) square Gamma (S-M(2)).
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    On decidability results of the holomorph of a finite cyclic group
    (Selcuk University Research Center of Applied Mathematics, 2008) Güzel, Eylem; Çevik, A. Sinan
    As a next step of the result in paper [1, Theorem 3.1], we study double coset separability, residually finitely and solvability of the power problem of holomorph of a finite cyclic group of order 2^{t}(t?Z?)in this paper.
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    On Kirchhoff Index and Resistance-Distance Energy of a Graph
    (Univ Kragujevac, Fac Science, 2012) Das, Kinkar Ch; Güngör, A. Dilek; Çevik, A. Sinan
    We report lower hounds for the Kirchhoff index of a connected (molecular) graph in terms of its structural parameters such as the number of vertices (atoms), the number of edges (bonds), maximum vertex degree (valency), second maximum vertex degree and minimum vertex degree. Also we give the Nordhaus-Gaddum-type result for Kirchhoff index. In this paper we define the resistance distance energy as the sum of the absolute values of the eigenvalues of the resistance distance matrix and also we obtain lower and upper bounds for this energy.
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    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, A. Dilek; Çevik, A. Sinan; Cangül, İsmail Naci
    In 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.
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    On the first Zagreb index and multiplicative Zagreb coindices of graphs
    (OVIDIUS UNIV PRESS, 2016) Das, Kinkar Ch; Akgüneş, Nihat; Togan, Müge; Yurttaş, Aysun; Cangül, I. Naci; Çevik, A. Sinan
    For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M-1(G) = Sigma v(i is an element of V(G))d(C)(v(i))(2), where d(G) (v(i)) is the degree of vertex v(i), in G. Recently Xu et al. introduced two graphical invariants (Pi) over bar (1) (G) = Pi v(i)v(j is an element of E(G)) (dG (v(i))+dG (v(j))) and (Pi) over bar (2)(G) = Pi(vivj is an element of E(G)) (dG (v(i))+dG (v(j))) named as first multiplicative Zagreb coindex and second multiplicative Zagreb coindex, respectively. The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G, that is, NK(G) = Pi(n)(i=1) d(G) (v(i)). The irregularity index t(G) of G is defined as the num=1 ber of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M-1(G) of graphs and trees in terms of number of vertices, irregularity index, maximum degree, and characterize the extremal graphs. Moreover, we obtain some lower and upper bounds on the (first and second) multiplicative Zagreb coindices of graphs and characterize the extremal graphs. Finally, we present some relations between first Zagreb index and NarumiKatayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.
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    On the Harary Energy and Harary Estrada Index of a Graph
    (Univ Kragujevac, Fac Science, 2010) Güngör, A. Dilek; Çevik, A. Sinan
    The main purposes of this paper are to introduce and investigate the Harary energy and Harary Estrada index of a graph. In addition we establish upper and lower bounds for these new energy and index separately.
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    On the Norms of Toeplitz and Hankel Matrices With Pell Numbers
    (Amer Inst Physics, 2010) Karpuz, Eylem Güzel; Ateş, Fırat; Güngör, A. Dilek; Cangül, İsmail Naci; Çevik, A. Sinan
    Let us define A = [a(ij)](i,j=0)(n-1) and B = [b(ij)](i,j=0)(n-1) as n x n Toeplitz and Hankel matrices, respectively, such that a(ij) = Pi-j and b(ij) = Pi+j, where P denotes the Pell number. We present upper and lower bounds for the spectral norms of these matrices.
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    Randic Matrix and Randic Energy
    (Univ Kragujevac, Fac Science, 2010) Bozkurt, Ş. Burcu; Güngör, A. Dilek; Gutman, Ivan; Çevik, A. Sinan
    If G is a graph on n vertices, and d(i) is the degree of its i-th vertex, then the Randic matrix of G is the square matrix of order n whose (i, j)-entry is equal to 1/root d(i) d(j) di if the i-th and j-th vertex of G are adjacent, and zero otherwise. This matrix in a natural way occurs within Laplacian spectral theory, and provides the non-trivial part of the so-called normalized Laplacian matrix. In spite of its obvious relation to the famous Randic index, the Randic matrix seems to have not been much studied in mathematical chemistry. In this paper we define the Randic energy as the sum of the absolute values of the eigenvalues of the Randic matrix, and establish mine of its properties, in particular lower and upper bounds for it.
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    Some properties on the tensor product of graphs obtained by monogenic semigroups
    (ELSEVIER SCIENCE INC, 2014) Akgüneş, Nihat; Das, Kinkar Ch.; Çevik, A. Sinan
    In Das et al. (2013) [8], a new graph 1'(S-M) on monogenic semigroups S-M (with zero) having elements {0, x, x(2), x(3),..., x(n)} has been recently defined. The vertices are the non-zero elements x; x(2); x(3);..., x(n) and, for 1 <= i,j <= n, any two distinct vertices x(i) and x(j) are adjacent if x(i)x(j) = 0 in S-M. As a continuing study, in Akgunes et al. (2014) [3], it has been investigated some well known indices (first Zagreb index, second Zagreb index, Randic index, geometric-arithmetic index, atom-bond connectivity index, Wiener index, Harary index, first and second Zagreb eccentricity indices, eccentric connectivity index, the degree distance) over Gamma(S-M). In the light of above references, our main aim in this paper is to extend these studies over Gamma(S-M) to the tensor product. In detail, we will investigate the diameter, radius, girth, maximum and minimum degree, chromatic number, clique number and domination number for the tensor product of any two (not necessarily different) graphs Gamma(S-M)(1) and Gamma(S-M(2)). (C) 2014 Published by Elsevier Inc.