Person: YURTTAŞ GÜNEŞ, AYSUN
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YURTTAŞ GÜNEŞ
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Publication 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; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0001-5349-3978; 0000-0002-0700-5774; A-6557-2018; AAG-8470-2021; J-3505-2017Graph 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.Publication Effect of edge deletion and addition on zagreb indices of graphs(Springer International Publishing Ag, 2019-01-01) Taş, K; Baleanu, D; Machado, JAT; Çevik, Ahmet Sinan; Togan, Muge; Yurttas, Aysun; YURTTAŞ GÜNEŞ, AYSUN; Cangül, Ismail Naci; CANGÜL, İSMAİL NACİ; Fen Edebiyat Fakültesi; Matematik Bölümü; Tas, K; Baleanu, D; Machado, JAT; 0000-0001-5349-3978; 0000-0002-7539-5065; 0000-0002-0700-5774; AAG-8470-2021; J-3505-2017Publication 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; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-0700-5774; 0000-0002-6439-8439; AAG-8470-2021; A-6557-2018; J-3505-2017Matching 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.Publication 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; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0001-5349-3978; 0000-0002-0700-5774; A-6557-2018; AAG-8470-2021; J-3505-2017Graph 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.Publication 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; 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-5098-2022Recently 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.Publication 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; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-0700-5774; A-6557-2018; J-3505-2017; AAG-8470-2021; FRC-3631-2022; EOF-7503-2022Cycloidal 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.Publication 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; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0001-5349-3978; 0000-0002-0700-5774; J-3505-2017; AAG-8470-2021Due 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.