Browsing by Author "Yurttaş, Aysun"

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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; 57189022403
The 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.
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; 57189022403
In [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.
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; 37090056000
In 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).
Deterrmining the minimal polynomial of cos(2π/n) over Q with Maple
(Amer Inst Physics, 2012) Simos, T. E.; Psihoyios, G.; Tsitouras, C.; Anastassi, Z.; Özgür, Birsen; Yurttaş, Aysun; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; AAG-8470-2021; J-3505-2017; ABA-6206-2020; ABI-4127-2020; 54403501400; 37090056000; 57189022403
The 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 and in some of these methods, the minimal polynomials of several algebraic numbers are used. Here we obtain the minimal polynomial of one of those numbers, cos(2 pi/n), over the field of rationals by means of the better known Chebycheff polynomials for odd q and give some of their properties. We calculated this minimal polynomial for n is an element of N by using the Maple language and classifying the numbers n is an element of N into different classes.
Graf operasyonlarının Zagreb ve çarpımsal Zagreb indeksleri
(Uludağ Üniversitesi, 2014) Yurttaş, Aysun; Cangül, İ. Naci; Özmutlu, Emin N.; Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı.
Bu çalışmada graf operasyonlarının birinci ve ikinci çarpımsal Zagreb indeksleri için bazı üst sınırlar verilmiştir. Bu tez altı bölümden oluşmaktadır. Birinci bölüm giriş bölümü olup bu bölümde konunun literatür özeti yapılmıştır. İkinci bölümde çalışmanın ilerleyen bölümlerinde kullanılacak olan bazı temel kavramlar tanıtılmış ve örnekler verilmiştir. Üçüncü bölümde birinci ve ikinci Zagreb ve çarpımsal Zagreb indeksleriyle eşindeksleri tanıtılmış ve elde edilen teorem ve sonuçlar verilmiştir. Dördüncü bölümde grafların birleşimi, toplamı, Kartezyen çarpımı, disjunctionı, corona çarpımı gibi graf operasyonları tanıtılmış ve bu işlemlerin bazı özellikleri verilmiştir. Beşinci bölümde dördüncü bölümde tanıtılan graf işlemlerinin birinci ve ikinci Zagreb indeksleri ve eşindeksleriyle ilgili teoremler verilmiştir. Altıncı ve son bölüm ise çalışmanın temeli olup grafların kartezyen çarpım, toplam, corona çarpım, disjunction, bileşim, simetrik fark gibi graf operasyonları için üst sınırlar elde edilmiş ve bazı iyi bilinen graflara uygulanmıştır. Bu bölümde verilen tüm sonuçlar bu tez çalışmasında elde edilmiş orijinal sonuçlardır.
Inverse problem for bell index
(Univ Nis, Fac Sci Math, 2020-01-01) Togan, Müge; Yurttaş, Aysun; YURTTAŞ GÜNEŞ, AYSUN; Şanlı, Utkum; Çelik, Feriha; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5349-3978; 0000-0002-0700-5774; J-3505-2017; AAG-8470-2021
Due to their applications in many branches of science, topological graph indices are becoming more popular every day. Especially as one can model chemical molecules by graphs to obtain valuable information about the molecules using solely mathematical calculations on the graph. The inverse problem for topological graph indices is a recent problem proposed by Gutman and is about the existence of a graph having its index value equal to a given non-negative integer. In this paper, the inverse problem for Bell index which is one of the irregularity indices is solved. Also a recently defined graph invariant called omega invariant is used to obtain several properties related to the Bell index.
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; 57189022403
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.
Inverse problem for Zagreb indices
(Springer, 2018-10-23) Lokesha, Veerebradiah; Gutman, Ivan; Yurttaş, Aysun; Togan, Müge; Cangül, İsmail Naci; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; AAG-8470-2021; 57204472437; 54403978300; 57189022403
The inverse problem for integer-valued topological indices is about the existence of a graph having its index value equal to a given integer. We solve this problem for the first and second Zagreb indices, and present analogous results also for the forgotten and hyper-Zagreb index. The first Zagreb index of connected graphs can take any even positive integer value, except 4 and 8. The same is true if one restricts to trees or to molecular graphs. The second Zagreb index of connected graphs can take any positive integer value, except 2, 3, 5, 6, 7, 10, 11, 13, 15 and 17. The same is true if one restricts to trees or to molecular graphs.
Kuantum kimyası ve grup teori
(Uludağ Üniversitesi, 2008) Yurttaş, Aysun; Cangül, İ. Naci; Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı.
Bu çalışmada Kuantum Kimyası ile Grup Teori arasındaki ilişkilere değinilmiştir. Matematik ve Kimyanın bir çok ortak noktasından biri de Grup Teorinin Kuantum Kimyasındaki uygulamalarıdır.Bu tezde moleküler simetriden başlanarak simetri kavramı tanımlanmış ve simetri elemanları ile işlemleri sınıflandırılmıştır. Fonksiyonların simetri özellikleri dönme grupları, simetri grupları ve direk çarpım grupları yardımıyla cebirsel olarak irdelenmiştir.
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; 57189022403
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.
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; 54403978300
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.
On the first Zagreb index and multiplicative Zagreb coindices of graphs
(Ovidius University, 2014-02-10) Das, Kinkar Ch; Akgüneş, Nihat; Çevik, A. Sinan; Togan, Müge; Yurttaş, Aysun; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; AAG-8470-2021; ABA-6206-2020; J-3505-2017; 54403978300; 37090056000; 57189022403
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.
Some formulae for the Zagreb indices of graphs
(Amer Inst Physics, 2012) Çevik, Ahmet Sinan; Simos, T. E.; Psihoyios, G.; Tsitouras, C.; Anastassi, Z.; Cangül, İsmail Naci; Yurttaş, Aysun; Togan, Müge; Uludaǧ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; AAG-8470-2021; J-3505-2017; ABA-6206-2020; 57189022403; 37090056000; 54403978300
In 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.
Some properties of the minimal polynomials of 2cos(pi/q) for odd q
(Amer Inst Pyhsics, 2011) Simos, T. E.; Özgür, Birsen; Demirci, Musa; Yurttaş, Aysun; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; ABI-4127-2020; J-3505-2017; AAG-8470-2021; 54403501400; 23566581100; 37090056000; 57189022403
The 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 this number by means of the better known Chebycheff polynomials for odd q and give some of their properties.
The effect of edge and vertex deletion on omega invariant
(Univ Belgrade, Fac Electrical Engineering, 2020-12-01) Delen, Sadık; Togan, Müge; Yurttaş, Aysun; Ana, Uğur; Cangül, İsmail Naci; Delen, Sadık; Togan, Müge; YURTTAŞ GÜNEŞ, AYSUN; Ana, Uğur; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0001-5349-3978; 0000-0002-0700-5774; AAG-8470-2021; J-3505-2017; EUU-3205-2022; GBL-2333-2022; CBI-5098-2022
Recently the first and last authors defined a new graph characteristic called omega related to Euler characteristic to determine several topological and combinatorial properties of a given graph. This new characteristic is defined in terms of a given degree sequence as a graph invariant and gives a lot of information on the realizability, number of realizations, connectedness, cyclicness, number of components, chords, loops, pendant edges, faces, bridges etc. of the family of realizations.In this paper, the effect of the deletion of vertices and edges from a graph on omega invariant is studied.
Upper bounds for the level of normal subgroups of Hecke groups
(Amer Inst Pyhsics, 2011) Simos, T. E.; Demirci, Musa; Yurttaş, Aysun; 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; AAG-8470-2021; 23566581100; 37090056000; 57189022403
In [4], 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. In this work we generalise these results to Hecke groups. We get results between three parameters of a normal subgroup, i.e. the index mu, the level n and the parabolic class number t. We deal with the case q = 4, and then obtain the generalisation to other q. Two main problems here are the calculation of the number of normal subgroups and the determination of the bounds on the level n for a given t.