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Öğe Generalization for Estrada Index(Amer Inst Physics, 2010) Güngör, Ayşe Dilek; Çevik, Ahmet Sinan; Karpuz, Eylem G.; Ateş, Fırat; Cangül, İsmail NaciIn 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.Öğe A new example of strongly pi inverse monoids(2011) Karpuz, Eylem Güzel; Çevik, Ahmet SinanIn [1], Ate¸s defined the semidirect product version of the Schützenberger product for any two monoids, and examined its regularity. Since this is a new product and there are so many algebraic properties that need to be checked for it, in this paper we determine necessary and sufficient conditions for this new version to be strongly pi-inverse, and then give some results.Öğe A presentation and some finiteness conditions for a new version of the schützenberger product of monoids(2016) Karpuz, Eylem Güzel; Ateş, Fırat; Çevik, Ahmet Sinan; Cangül, İsmail NaciIn this paper we first define a new version of the Sch¨utzenberger 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.Öğe Primes in Z[exp(2?i/3)](Amer Inst Physics, 2010) Namlı, Dilek; Cangül, İsmail Naci; Çevik, Ahmet Sinan; Güngör, A. Dilek; Tekcan, AhmetIn this paper, we study the primes in the ring Z[w], where w = exp(2 pi i/3) is a cubic root of unity. We gave a classification of them and some results related to the use of them in the calculation of cubic residues are obtained.Öğe Rewriting as a Special Case of Noncommutative Gröbner Bases Theory for the Affine Weyl Group An(Birkhauser Boston, 2010) Çevik, Ahmet Sinan; Özel, Cenap; Karpuz, Eylem GüzelThe aim of this work is to find Grobner-Shirshov bases of the affine Weyl group of type (A(n)) over tilde (n >= 2) from the point of complete rewriting systems.Öğe Some Formulae for the Zagreb Indices of Graphs(AMER INST PHYSICS, 2012) Cangül, İsmail Naci; Yurttaş, Aysun; Togan, Müge; Çevik, Ahmet SinanIn this study, we first find formulae for the first and second Zagreb indices and coindices of certain classical graph types including path, cycle, star and complete graphs. Secondly we give similar formulae for the first and second Zagreb coindices.Öğe Some properties on the lexicographic product of graphs obtained by monogenic semigroups(SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Akgüneş, Nihat; Das, Kinkar C.; Çevik, Ahmet Sinan; Cangül, İsmail NaciIn (Das et al. in J. Inequal. Appl. 2013:44, 2013), a new graph Gamma (S-M) on monogenic semigroups S-M (with zero) having elements {0, x, x(2), x(3),..., x(n)} was 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 an unpublished work, 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) were investigated by the same authors of this paper. In the light of the above references, our main aim in this paper is to extend these studies to the lexicographic product over Gamma (S-M). In detail, we investigate the diameter, radius, girth, maximum and minimum degree, chromatic number, clique number and domination number for the lexicographic product of any two (not necessarily different) graphs Gamma (S-M(1)) and Gamma (S-M(2)).
