Browsing by Author "DEMİRCİ, MUSA"

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A class of congruence subgroups of hecke group H ( λ 5)
(Acad Sinica, 2006-12-01) Demirci, Musa; Cangül, İsmail Naci; DEMİRCİ, MUSA; CANGÜL, İSMAİL NACİ; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-0700-5774; A-6557-2018; J-3505-2017
In [2], it is shown that, for some Hecke groups, unlike the modular group, two definitions of the principal congruence subgroups may not coincide and congruence and principal congruence subgroups of two important Hecke groups H (SICm), for m = 2 or 3, are classified and the quotients of H (SICm) with these normal subgroups are given. Here we obtain a classification of the congruence subgroups obtained as the kernel of reduction homomorphism for another important Hecke group H (lambda(5)) and also obtain the quotient groups. Finally the indices and abstract group structure of all these subgroups are determined.
A constructive method for the cycloidal normal free subgroups of finite index of hecke groups H (√2) AND H (√3)
(Acad Sinica, 2006-09-01) DOĞAN, SETENAY; DEMİRCİ, MUSA; Demirci, Musa; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bizim, Osman; BİZİM, OSMAN; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; A-6557-2018; AAH-1468-2021; AAH-9762-2021; J-3505-2017; ABA-6206-2020
Cycloidal subgrups of the modular group are studied in [8]. Here cycloidal free normal subgroups of Hecke groups are considered. It is found that when q equivalent to 2 ( mod 4), H ( lambda(q)) has no such subgroups. In all other cases the signatures of these subgroups are constructed by means of q-gons and their signatures are given.
Construction of cycloidal free subgroups of hecke groups of finite index
(Pushpa Publishing House, 2009-08-01) Yurttaş, Aysun; Demirci, Musa; Özbay, Hatice; Çapkın, Müge; Cangul, İsmail Naci; YURTTAŞ GÜNEŞ, AYSUN; DEMİRCİ, MUSA; Özbay, Hatice; Çapkın, Müge; CANGÜL, İSMAİL NACİ; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; A-6557-2018; J-3505-2017; AAG-8470-2021; FRC-3631-2022; EOF-7503-2022
Cycloidal subgroups of the modular group are studied in [7]. Cycloidal normal subgroups of the Hecke groups, which are generalisations of the modular group, are studied in [2]. Here we study cycloidal free subgroups of Hecke groups. These are subgroups with signature (g; infinity). Here these subgroups are given by their signatures for q = 4, 5, 6 first, and then for all q. It is found that when q equivalent to 2 mod 4, H(lambda(q)) has no cycloidal free subgroups.
Corrigendum on "the number of points on elliptic curves E : y2 = x3
(Korean Mathematical Soc, 2007-01-01) İnam, İlker; Soydan, Gökhan; SOYDAN, GÖKHAN; CANGÜL, İSMAİL NACİ; Bizim, Osman; BİZİM, OSMAN; Demirci, Musa; DEMİRCİ, MUSA; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0001-5765-1718; 0000-0002-0700-5774; M-9459-2017; ABA-6206-2020; A-6557-2018; AAH-1468-2021
In this work, authors considered a result concerning elliptic curves y(2) = x(3) + ex over F-p mod 8, given at [1]. They noticed that there should be a slight change at this result. They give counterexamples and the correct version of the result.
Harmonic index and zagreb indices of vertex-semitotal graphs
(New York Business Global Llc, 2020-01-01) Günes, Aysun Yurttaş; YURTTAŞ GÜNEŞ, AYSUN; Togan, Muge; Demirci, Musa; DEMİRCİ, MUSA; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0001-5349-3978; 0000-0002-0700-5774; A-6557-2018; AAG-8470-2021; J-3505-2017
Graph theory is one of the rising areas in mathematics due to its applications in many areas of science. Amongst several study areas in graph theory, spectral graph theory and topological descriptors are in front rows. These descriptors are widely used in QSPR/QSAR studies in mathematical chemistry. Vertex-semitotal graphs are one of the derived graph classes which are useful in calculating several physico-chemical properties of molecular structures by means of molecular graphs modelling the molecules. In this paper, several topological descriptors of vertex-semitotal graphs are calculated. Some new relations on these values are obtained by means of a recently defined graph invariant called omega invariant.
Inverse problem for albertson irregularity index
(Turkic World Mathematical Soc, 2022-01-01) Güneş, Aysun; YURTTAŞ GÜNEŞ, AYSUN; Togan, M.; Demirci, Musa; DEMİRCİ, MUSA; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5349-3978; 0000-0002-0700-5774; A-6557-2018; AAG-8470-2021; J-3505-2017
Graph indices have attracted great interest as they give us numerical clues for several properties of molecules. Some indices give valuable information on the molecules under consideration using mathematical calculations only. For these reasons, the calculation and properties of graph indices have been in the center of research. Naturally, the values taken by a graph index is an important problem called the inverse problem. It requires knowledge about the existence of a graph having index equal to a given number. The inverse problem is studied here for Albertson irregularity index as a part of investigation on irregularity indices. A class of graphs is constructed to show that the Albertson index takes all positive even integers. It has been proven that there exists at least one tree with Albertson index equal to every even positive integer but 4. The existence of a unicyclic graph with irregularity index equal to m is shown for every even positive integer m except 4. It is also shown that the Albertson index of a cyclic graph can attain any even positive integer.
Matching number and characteristic polynomial of a graph
(Taylor & Francis, 2020-07-11) Yurttaş Güneş, Aysun; Demirci, Musa; Öz, Mert Sinan; Cangül, İsmail Naci; YURTTAŞ GÜNEŞ, AYSUN; DEMİRCİ, MUSA; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-6439-8439; AAG-8470-2021; A-6557-2018; J-3505-2017
Matching number and the spectral properties depending on the characteristic polynomial of a graph obtained by means of the adjacency polynomial has many interesting applications in different areas of science. There are some work giving the relation of these two areas. Here the relations between these two notions are considered and several general results giving this relations are obtained. A result given for only unicyclic graphs is generalized. There are some methods for determining the matching number of a graph in literature. Usually nullity, spanning trees and several graph parts are used to do this. Here, as a new method, the conditions for calculating the matching number of a graph by means of the coefficients of the characteristic polynomial of the graph are determined. Finally some results on the matching number of graphs are obtained.
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-3505-2017
A 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.
On omega index and average degree of graphs
(Hindawi, 2021-11-12) Delen, Sadık; Demirci, Musa; Cevik, Ahmet Sinan; Cangül, İsmail Naci; Delen, Sadık; DEMİRCİ, MUSA; CANGÜL, İSMAİL NACİ; 0000-0002-0700-5774; 0000-0002-6439-8439; 0000-0003-4689-3660; A-6557-2018; J-3505-2017; EUU-3205-2022
Average degree of a graph is defined to be a graph invariant equal to the arithmetic mean of all vertex degrees and has many applications, especially in determining the irregularity degrees of networks and social sciences. In this study, some properties of average degree have been studied. Effect of vertex deletion on this degree has been determined and a new proof of the handshaking lemma has been given. Using a recently defined graph index called omega index, average degree of trees, unicyclic, bicyclic, and tricyclic graphs have been given, and these have been generalized to k-cyclic graphs. Also, the effect of edge deletion has been calculated. The average degree of some derived graphs and some graph operations have been determined.
On the conjecture of jesmanowicz
(Centre Environment Social & Economic Research Publ-ceser, 2017-01-01) Togbe, Alain; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Soydan, Gokhan; SOYDAN, GÖKHAN; Demirci, Musa; DEMİRCİ, MUSA; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-5882-936X; J-3505-2017; A-6557-2018; ABA-6206-2020; M-9459-2017
We give a survey on some results covering the last 60 years concerning Jesmanowicz' conjecture. Moreover, we conclude the survey with a new result by showing that the special Diophantine equation(20k)(x) + (99k)(y) = (101k)(z)has no solution other than (x, y, z) = (2, 2, 2).
The group structure of frey elliptic curves over finite fields FP (Retracted article)
(Bulgarian Acad Science, 2007-01-01) İkikardeş, Nazlı Yıldız; Demirci, Musa; DEMİRCİ, MUSA; Soydan, Gökhan; SOYDAN, GÖKHAN; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-6321-4132; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; A-6557-2018
Frey elliptic curves are the curves (y2) = x(3) - n(2)x and in this work the group structure E(F-p) of these curves over finite fields Fp is considered.This gioup structure and the number of points on these elliptic curves depend on the existence of elements of order 4. Therefore the cases where the group of the curve has such elements are determined. It is also shown that the number of such elements, if an, is either 4 or 12. Classification is made according to n is a quadratic residue or not.