http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
New Relations for the Normal Subgroups of Hecke Groups
Musa DEMIRCI,Osman AKBAYRAK,Aydin OZBEK,Ugur ANA 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.2
For an integer q ≥ 3, Hecke groups H(λq) are an important class of discrete groups with the most important member being the famous modular group obtained in the case of q = 3. They were defined by E. Hecke in 1936 when he was studying with Dirichlet series. There are a number of research papers on the properties of Hecke groups, their normal subgroups and the relation with regular maps. Here we add some recent results to state new relations between the parameters of the normal subgroups of Hecke groups and the corresponding regular maps which are also graphs in combinatorial sense by means of a new graph invariant called omega which was recently defined in 2018.
CHARACTERISTIC POLYNOMIALS OF SUBDIVISION GRAPHS
FERIHA CELIK,Musa DEMIRCI,SADIK DELEN,Ugur ANA,Ismail Naci CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.1
Energy of a graph, rstly dened by E. Huckel is an important sub area of graph theory with numerous applications in Chemistry and Physics together with all areas they are used as fundamental methods. Schrodinger equation is a second order dierential equation which include the energy of the corresponding system. Subdivision of a graph is a method of obtaining a derived graph from a given one which helps to calculate some properties of a complex molecular graph by calculating the same for some easier molecular graph. Unlike many other areas in graph theory, to obtain a general result in spectral graph theory is indeed quite dicult and mostly impossible. In this article, as a result of this idea, the spectral polynomials and their reccurence relations of the subdivision graphs of some well-known graphs are studied. Also the energy of some subdivision graphs are obtained by using the denition of energy. A new relation for the characteristic polynomial of a cyclic graph in terms of the triangular numbers is also obtained.
Omega Invariant of Union, Join and Corona Product of Two Graphs
Merve ASCIOGLU,Musa DEMIRCI,Ismail Naci CANGUL 장전수학회 2020 Advanced Studies in Contemporary Mathematics Vol.30 No.3
Graphs nowadays are getting a lot of attention due to their applications in all areas of science including physics, chemistry, pharmacology, network science, neuroscience, social sciences, etc. There are several mathematical methods used in graph theory to obtain such applications. Nearly in half of them, the vertex degrees and the degree sequences play an important role. The graph products are very useful tools as they help us to calculate several properties of large graphs by means of smaller graphs. Recently, a new topological graph invariant named as omega was defined in terms of the vertex degrees, that is degree sequence. In this paper, the degree sequences of the union of some special graph classes are given. Recalling the degree sequences of the join and corona products of two special graph classes from literature, the omega invariants of the union, join and corona products of two special graphs are obtained. Also for each of these graph products, results giving the omega values and the number of faces for general graphs are given.
A method for finding normal subgroups of Hecke groups
Hasan Basri Özdemir,Musa Demirci,Ismail Naci Cangül 장전수학회 2006 Proceedings of the Jangjeon mathematical society Vol.9 No.1
Hecke groups, being discrete groups, play an important role in abstract group theory and number theory. Their normal subgroups are studied in [2]: Here, using a result of D. Singerman [7]; we deduce a method of nding normal subgroups of all Hecke groups. This method helps us to obtain the signature of these subgroups, and their abstract group structure can be obtained from this by means of the results in [1]: As a result, the abstract group structure of normal subgroups of Hecke groups corresponding to cyclic and dihedral quotients is obtained.1
Inam, Ilker,Soydan, Gokhan,Demirci, Musa,BiZim, Osman,Cangul, Ismail Naci Korean Mathematical Society 2007 대한수학회논문집 Vol.22 No.2
In this work, authors considered a result concerning elliptic curves $y^2=x^3+cx$ over $\mathbb{F}_p$ 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.