şerife büyükköse - Academia.edu (original) (raw)

Papers by şerife büyükköse

Research paper thumbnail of A Note on the Weighted Wiener Index and the Weighted Quasi Wiener Index

gazi university journal of science, Dec 11, 2017

In this study, we consider the weighted Wiener index and the weighted quasi-Wiener index of simpl... more In this study, we consider the weighted Wiener index and the weighted quasi-Wiener index of simple connected weighted graphs and we find some bounds for the weighted Wiener index and the weighted quasi-Wiener index of the weighted graphs. Moreover, we obtain some results by using these bounds for weighted and unweighted graphs.

Research paper thumbnail of The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs

DergiPark (Istanbul University), Dec 16, 2015

In this study, we find an upper bound for the largest signless Laplacian eigenvalue of simple con... more In this study, we find an upper bound for the largest signless Laplacian eigenvalue of simple connected weighted graphs, where edge weights are positive definite square matrices. Also we obtain some results on weighted and unweighted graphs by using this bound.

Research paper thumbnail of Graph operations of Randic index

Nucleation and Atmospheric Aerosols, 2018

The Randic index R(G) of a graph G whose vertex i and j has degree di and dj respectively is defi... more The Randic index R(G) of a graph G whose vertex i and j has degree di and dj respectively is defined by sum of the 1/didj if the vertices i and j are adjacent. We introduce the weighted Randic index, we establish basic mathematical properties of Randic index and we investigate its behavior under some graph operations in this paper.

Research paper thumbnail of A proof of a conjecture on monotonic behavior of the largest eigenvalue of a number-theoretic matrix

Nucleation and Atmospheric Aerosols, 2015

In this study we investigate the monotonic behavior of the largest eigenvalue of the n×n matrix E... more In this study we investigate the monotonic behavior of the largest eigenvalue of the n×n matrix EnTEn, where the i j− entry of En is 1 if j|i and 0 otherwise and hence we present a proof of a part of the Mattila-Haukkanen conjecture [16]. MSC2010. 15A18, 15A42, 11A25

Research paper thumbnail of Determinants and inverses of circulant matrices with complex Fibonacci numbers

Special Matrices, Jan 24, 2015

In the present paper we calculate the determinant of Fn in terms of complex Fibonacci numbers. Fu... more In the present paper we calculate the determinant of Fn in terms of complex Fibonacci numbers. Furthermore, we show that Fn is invertible and obtain the entries of the inverse of Fn in terms of complex Fibonacci numbers.

Research paper thumbnail of A proof of a conjecture on monotonic behavior of the smallest and the largest eigenvalues of a number theoretic matrix

Linear Algebra and its Applications, Apr 1, 2015

In this study we investigate the monotonic behavior of the smallest eigenvalue t n and the larges... more In this study we investigate the monotonic behavior of the smallest eigenvalue t n and the largest eigenvalue T n of the n × n matrix E T n E n , where the ij-entry of E n is 1 if j | i and 0 otherwise. We present a proof of the Mattila-Haukkanen conjecture which states that for every n ∈ Z + , t n+1 ≤ t n and T n ≤ T n+1. Also, we prove that lim n→∞ t n = 0 and limn→∞ T n = ∞ and we give a lower bound for t n .

Research paper thumbnail of Graphic representation of open and distance education history

Global Journal of Information Technology, Dec 24, 2017

Nowada ys , learning a nd ins tructi on take place i ndependent of ti me and spa ce through the d... more Nowada ys , learning a nd ins tructi on take place i ndependent of ti me and spa ce through the dis tance educa tion s ys tem, wherein courses a re conducted completel y online through network technologies using intera cti ve video-based ins tructional ma terials. This s tudy examines the open and dis tance educati on s ys tem tha t was a pa rt of the his tory of educa tion in the Turkish republi c fi rs t a t uni versi ties, and then in high s ch ools and seconda ry s chools. It is aimed to na rra te the history of open and dis tance educa tion using graph theory trees in order to provi de a better unders tanding of this process. Wi thin this context, the project YAYÇEP ma y be mentioned. Histori cal developments can be na rra ted in a chronological order through graph theory trees , and this makes it possible to see the bi g pi cture. Open and distance educa tion is dis cussed, his torical informa tion is gi ven and, fi nally, a graph theory tree dra wn using the graph theory is used to explain the topi c.

Research paper thumbnail of Ağırlıklı Enerji İçin Bazı Sınırlar

Sinop Üniversitesi fen bilimleri dergisi, Dec 25, 2012

Energy of a graph is a concept defined in 1978 and originated from theoretical chemistry. Recentl... more Energy of a graph is a concept defined in 1978 and originated from theoretical chemistry. Recently, the energy, Laplacian energy, signless Laplacian energy and normalized Laplacian energy of a graph have received much interest. In short, for an n-vertex connected unweighted graph G, the energy is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. For a simple connected matrix weighted graph G, the weighted energy is defined as the sum of the absolute values of the eigenvalues of its weighted adjacency matrix. In this paper, a brief overview for the notations and concepts of matrix weighted and number weighted graphs that will be used throughout this study is given. In the Main results section, the weighted energy of simple connected matrix weighted graphs are considered and some bounds for the weighted energy are found. Also, some results on number weighted and unweighted graphs are obtained by means of these bounds.

Research paper thumbnail of On the bounds for the largest Laplacian eigenvalues of weighted graphs

Discrete Optimization, May 1, 2012

We consider weighted graphs, such as graphs where the edge weights are positive definite matrices... more We consider weighted graphs, such as graphs where the edge weights are positive definite matrices. The Laplacian eigenvalues of a graph are the eigenvalues of the Laplacian matrix of a graph G. We obtain an upper bound for the largest Laplacian eigenvalue and we compare this bound with previously known bounds.

Research paper thumbnail of The new upper bounds on the spectral radius of weighted graphs

Applied Mathematics and Computation, 2012

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalu... more We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain another upper bound which is sharp on the spectral radius of the adjacency matrix and compare with some known upper bounds with the help of some examples of graphs. We also characterize graphs for which the bound is attained.

Research paper thumbnail of On bounds for the smallest and the largest eigenvalues of GCD and LCM matrices

Mathematical Inequalities & Applications, 2016

In this paper, improving a famous result of Wolkowicz and Styan for the GCD matrix (S n) and the ... more In this paper, improving a famous result of Wolkowicz and Styan for the GCD matrix (S n) and the LCM matrix [S n ] defined on S n = {1,2,... ,n} , we present new upper and lower bounds for the smallest and the largest eigenvalues of (S n) and [S n ] in terms of particular arithmetical functions.

Research paper thumbnail of Examining The Concept Maps That Located In MONE The Educatıon Information Network

Kavram, bir nesnenin zihindeki soyut ve genel tasarımıdır. Kavram haritaları zihnin kavramları da... more Kavram, bir nesnenin zihindeki soyut ve genel tasarımıdır. Kavram haritaları zihnin kavramları daha kolay anlayabilmesi için tasarlanmış öğrenme araçlarıdır. Bu çalışmada Millî Eğitim Bakanlığı(MEB) Yenilik ve Eğitim Teknolojileri Genel Müdürlüğü'nün(YEĞİTEK) yürüttüğü bir proje sonucunda ortaya çıkan Eğitim Bilişim Ağı(EBA) üzerinden yayınlanmış olan kavram haritaları üzerine çalışılmıştır. Eğitim-öğretim sürecinde bilişim teknolojisi donanımlarını kullanarak etkin materyaller kullanılması amacıyla YEĞİTEK tarafından tasarlanan EBA sınıf seviyelerine uygun, güvenilir ve incelemeden geçmiş doğru e-içerikleri barındıran sosyal bir platformdur. Araştırma betimsel araştırma yöntemlerinden olan doküman inceleme yoluyla hazırlanmıştır. Araştırmanın evrenini EBA'da bulunan Tarih, Kimya, Felsefe, Fen Bilimleri, Arapça ve Türkçe alanlarında hazırlanmış on yedi adet kavram haritası oluşturmaktadır. Araştırmanın amacı EBA'da yayınlanan kavram haritalarının değerlendirilmesinin yapılmasıdır. Konuyla ilgili çalışma esnasında alan uzmanlarının görüşlerine başvurulmuştur. Elde edilen veriler ışığında toplam 17 kavram haritasından sadece 2 tanesinin hem kavram haritası değerlendirme ölçütlerine hem de materyal tasarlama ilkeleri doğrultusunda bütün maddelere uygun bulunduğu tespit edilmiştir.

Research paper thumbnail of Determinants of Circulant Matrices with Some Certain Sequences

gazi university journal of science, Feb 23, 2015

Let ሼ ሽ be a sequence of real numbers defined by an th order linear homogenous recurrence relatio... more Let ሼ ሽ be a sequence of real numbers defined by an th order linear homogenous recurrence relation. In this paper we obtain a determinant formula for the circulant matrix ൌ ሺ , , ⋯ , ሻ, providing a generalization of determinantal results in papers of Bozkurt [2], Bozkurt and Tam [3], and Shen, et al. [8].

Research paper thumbnail of Millî Eğitim Bakanlığı Eğitim Bilişim Ağı’nda Bulunan Kavram Haritalarının İncelenmesi

Kavram, bir nesnenin zihindeki soyut ve genel tasarimidir. Kavram haritalari zihnin kavramlari da... more Kavram, bir nesnenin zihindeki soyut ve genel tasarimidir. Kavram haritalari zihnin kavramlari daha kolay anlayabilmesi icin tasarlanmis ogrenme araclaridir. Bu calismada Milli Egitim Bakanligi(MEB) Yenilik ve Egitim Teknolojileri Genel Mudurlugu’nun(YEĞITEK) yuruttugu bir proje sonucunda ortaya cikan Egitim Bilisim Agi(EBA) uzerinden yayinlanmis olan kavram haritalari uzerine calisilmistir. Egitim-ogretim surecinde bilisim teknolojisi donanimlarini kullanarak etkin materyaller kullanilmasi amaciyla YEĞITEK tarafindan tasarlanan EBA sinif seviyelerine uygun, guvenilir ve incelemeden gecmis dogru e-icerikleri barindiran sosyal bir platformdur. Arastirma betimsel arastirma yontemlerinden olan dokuman inceleme yoluyla hazirlanmistir. Arastirmanin evrenini EBA’da bulunan Tarih, Kimya, Felsefe, Fen Bilimleri, Arapca ve Turkce alanlarinda hazirlanmis on yedi adet kavram haritasi olusturmaktadir. Arastirmanin amaci EBA’da yayinlanan kavram haritalarinin degerlendirilmesinin yapilmasidir. Konuyla ilgili calisma esnasinda alan uzmanlarinin goruslerine basvurulmustur. Elde edilen veriler isiginda toplam 17 kavram haritasindan sadece 2 tanesinin hem kavram haritasi degerlendirme olcutleri ne hem de materyal tasarlama ilkeleri dogrultusunda butun maddelere uygun bulundugu tespit edilmistir.

Research paper thumbnail of The Bounds for Eigenvalues of Normalized and Signless Laplacian Matrices

arXiv (Cornell University), Aug 25, 2014

In this paper, we obtain the bounds of the extreme eigenvalues of a normalized and signless Lapla... more In this paper, we obtain the bounds of the extreme eigenvalues of a normalized and signless Laplacian matrices using by their traces. In addition, we determine the bounds for k-th eigenvalues of normalized and signless Laplacian matrices.

Research paper thumbnail of Bounds for various graph energies

ITM web of conferences, 2022

In this paper, we obtain some upper and lower bounds for the spectral radius of some special matr... more In this paper, we obtain some upper and lower bounds for the spectral radius of some special matrices such as maximum degree, minimum degree, Randic, sum-connectivity, degree sum, degree square sum, first Zagreb and second Zagreb matrices of a simple connected graph G by the help of matrix theory. We also get some upper bounds for the corresponding energies of G.

Research paper thumbnail of Graphs Associated with Number Sequences

Research paper thumbnail of Lower and Upper Bounds for Some Degree-Based Indices of Graphs

In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced 1... more In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced 1 reciprocal Randic index, Narumi-Katayama index and symmetric division index a graph using solely the 2 vertex degrees. Then we obtain upper and lower bounds for these indices for the complete graphs, path 3 graphs and Fibonacci-sum graphs. Finally, we compared the bounds of these indices for a general graph 4 and some special graphs.

Research paper thumbnail of Bir Grafın GCD Enerjisi İçin Sınırlar

Zenodo (CERN European Organization for Nuclear Research), Nov 30, 2021

Öne Çıkanlar • Bu çalışmada Sayılar Teorisi'nde önemli bir kavram olan GCD (En büyük ortak bölen)... more Öne Çıkanlar • Bu çalışmada Sayılar Teorisi'nde önemli bir kavram olan GCD (En büyük ortak bölen) kavramı Graf Teori'ye taşınarak, grafın derecelerinin en büyük ortak bölenleri kullanılarak bir grafın GCD matrisi tanımlanmıştır. • Tanımlanan grafın GCD matrisinin en büyük özdeğeri (spectral yarıçapı) için alt ve üst sınır verilmiştir. • GCD matrisinin özellikleri göz önüne alınarak bu matrisin enerjisi için bir üst sınır elde edilmiştir. • Bazı özel grafların GCD matrisleri için sonuçlar elde edilmiştir.

Research paper thumbnail of Bir Grafın GCD Spektral Yarıçapı ve GCD Enerjisi İçin Alt ve Üst Sınırlar

Zenodo (CERN European Organization for Nuclear Research), Nov 30, 2021

Öne Çıkanlar • Bir grafın GCD matrisinin en büyük özdeğeri (spectral yarıçapı) için alt ve üst sı... more Öne Çıkanlar • Bir grafın GCD matrisinin en büyük özdeğeri (spectral yarıçapı) için alt ve üst sınır verilmiştir. • GCD matrisinin özellikleri göz önüne alınarak bu matrisin enerjisi için bir üst sınır elde edilmiştir. • Bazı özel grafların GCD matrisleri için sonuçlar elde edilmiştir.

Research paper thumbnail of A Note on the Weighted Wiener Index and the Weighted Quasi Wiener Index

gazi university journal of science, Dec 11, 2017

In this study, we consider the weighted Wiener index and the weighted quasi-Wiener index of simpl... more In this study, we consider the weighted Wiener index and the weighted quasi-Wiener index of simple connected weighted graphs and we find some bounds for the weighted Wiener index and the weighted quasi-Wiener index of the weighted graphs. Moreover, we obtain some results by using these bounds for weighted and unweighted graphs.

Research paper thumbnail of The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs

DergiPark (Istanbul University), Dec 16, 2015

In this study, we find an upper bound for the largest signless Laplacian eigenvalue of simple con... more In this study, we find an upper bound for the largest signless Laplacian eigenvalue of simple connected weighted graphs, where edge weights are positive definite square matrices. Also we obtain some results on weighted and unweighted graphs by using this bound.

Research paper thumbnail of Graph operations of Randic index

Nucleation and Atmospheric Aerosols, 2018

The Randic index R(G) of a graph G whose vertex i and j has degree di and dj respectively is defi... more The Randic index R(G) of a graph G whose vertex i and j has degree di and dj respectively is defined by sum of the 1/didj if the vertices i and j are adjacent. We introduce the weighted Randic index, we establish basic mathematical properties of Randic index and we investigate its behavior under some graph operations in this paper.

Research paper thumbnail of A proof of a conjecture on monotonic behavior of the largest eigenvalue of a number-theoretic matrix

Nucleation and Atmospheric Aerosols, 2015

In this study we investigate the monotonic behavior of the largest eigenvalue of the n×n matrix E... more In this study we investigate the monotonic behavior of the largest eigenvalue of the n×n matrix EnTEn, where the i j− entry of En is 1 if j|i and 0 otherwise and hence we present a proof of a part of the Mattila-Haukkanen conjecture [16]. MSC2010. 15A18, 15A42, 11A25

Research paper thumbnail of Determinants and inverses of circulant matrices with complex Fibonacci numbers

Special Matrices, Jan 24, 2015

In the present paper we calculate the determinant of Fn in terms of complex Fibonacci numbers. Fu... more In the present paper we calculate the determinant of Fn in terms of complex Fibonacci numbers. Furthermore, we show that Fn is invertible and obtain the entries of the inverse of Fn in terms of complex Fibonacci numbers.

Research paper thumbnail of A proof of a conjecture on monotonic behavior of the smallest and the largest eigenvalues of a number theoretic matrix

Linear Algebra and its Applications, Apr 1, 2015

In this study we investigate the monotonic behavior of the smallest eigenvalue t n and the larges... more In this study we investigate the monotonic behavior of the smallest eigenvalue t n and the largest eigenvalue T n of the n × n matrix E T n E n , where the ij-entry of E n is 1 if j | i and 0 otherwise. We present a proof of the Mattila-Haukkanen conjecture which states that for every n ∈ Z + , t n+1 ≤ t n and T n ≤ T n+1. Also, we prove that lim n→∞ t n = 0 and limn→∞ T n = ∞ and we give a lower bound for t n .

Research paper thumbnail of Graphic representation of open and distance education history

Global Journal of Information Technology, Dec 24, 2017

Nowada ys , learning a nd ins tructi on take place i ndependent of ti me and spa ce through the d... more Nowada ys , learning a nd ins tructi on take place i ndependent of ti me and spa ce through the dis tance educa tion s ys tem, wherein courses a re conducted completel y online through network technologies using intera cti ve video-based ins tructional ma terials. This s tudy examines the open and dis tance educati on s ys tem tha t was a pa rt of the his tory of educa tion in the Turkish republi c fi rs t a t uni versi ties, and then in high s ch ools and seconda ry s chools. It is aimed to na rra te the history of open and dis tance educa tion using graph theory trees in order to provi de a better unders tanding of this process. Wi thin this context, the project YAYÇEP ma y be mentioned. Histori cal developments can be na rra ted in a chronological order through graph theory trees , and this makes it possible to see the bi g pi cture. Open and distance educa tion is dis cussed, his torical informa tion is gi ven and, fi nally, a graph theory tree dra wn using the graph theory is used to explain the topi c.

Research paper thumbnail of Ağırlıklı Enerji İçin Bazı Sınırlar

Sinop Üniversitesi fen bilimleri dergisi, Dec 25, 2012

Energy of a graph is a concept defined in 1978 and originated from theoretical chemistry. Recentl... more Energy of a graph is a concept defined in 1978 and originated from theoretical chemistry. Recently, the energy, Laplacian energy, signless Laplacian energy and normalized Laplacian energy of a graph have received much interest. In short, for an n-vertex connected unweighted graph G, the energy is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. For a simple connected matrix weighted graph G, the weighted energy is defined as the sum of the absolute values of the eigenvalues of its weighted adjacency matrix. In this paper, a brief overview for the notations and concepts of matrix weighted and number weighted graphs that will be used throughout this study is given. In the Main results section, the weighted energy of simple connected matrix weighted graphs are considered and some bounds for the weighted energy are found. Also, some results on number weighted and unweighted graphs are obtained by means of these bounds.

Research paper thumbnail of On the bounds for the largest Laplacian eigenvalues of weighted graphs

Discrete Optimization, May 1, 2012

We consider weighted graphs, such as graphs where the edge weights are positive definite matrices... more We consider weighted graphs, such as graphs where the edge weights are positive definite matrices. The Laplacian eigenvalues of a graph are the eigenvalues of the Laplacian matrix of a graph G. We obtain an upper bound for the largest Laplacian eigenvalue and we compare this bound with previously known bounds.

Research paper thumbnail of The new upper bounds on the spectral radius of weighted graphs

Applied Mathematics and Computation, 2012

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalu... more We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain another upper bound which is sharp on the spectral radius of the adjacency matrix and compare with some known upper bounds with the help of some examples of graphs. We also characterize graphs for which the bound is attained.

Research paper thumbnail of On bounds for the smallest and the largest eigenvalues of GCD and LCM matrices

Mathematical Inequalities & Applications, 2016

In this paper, improving a famous result of Wolkowicz and Styan for the GCD matrix (S n) and the ... more In this paper, improving a famous result of Wolkowicz and Styan for the GCD matrix (S n) and the LCM matrix [S n ] defined on S n = {1,2,... ,n} , we present new upper and lower bounds for the smallest and the largest eigenvalues of (S n) and [S n ] in terms of particular arithmetical functions.

Research paper thumbnail of Examining The Concept Maps That Located In MONE The Educatıon Information Network

Kavram, bir nesnenin zihindeki soyut ve genel tasarımıdır. Kavram haritaları zihnin kavramları da... more Kavram, bir nesnenin zihindeki soyut ve genel tasarımıdır. Kavram haritaları zihnin kavramları daha kolay anlayabilmesi için tasarlanmış öğrenme araçlarıdır. Bu çalışmada Millî Eğitim Bakanlığı(MEB) Yenilik ve Eğitim Teknolojileri Genel Müdürlüğü'nün(YEĞİTEK) yürüttüğü bir proje sonucunda ortaya çıkan Eğitim Bilişim Ağı(EBA) üzerinden yayınlanmış olan kavram haritaları üzerine çalışılmıştır. Eğitim-öğretim sürecinde bilişim teknolojisi donanımlarını kullanarak etkin materyaller kullanılması amacıyla YEĞİTEK tarafından tasarlanan EBA sınıf seviyelerine uygun, güvenilir ve incelemeden geçmiş doğru e-içerikleri barındıran sosyal bir platformdur. Araştırma betimsel araştırma yöntemlerinden olan doküman inceleme yoluyla hazırlanmıştır. Araştırmanın evrenini EBA'da bulunan Tarih, Kimya, Felsefe, Fen Bilimleri, Arapça ve Türkçe alanlarında hazırlanmış on yedi adet kavram haritası oluşturmaktadır. Araştırmanın amacı EBA'da yayınlanan kavram haritalarının değerlendirilmesinin yapılmasıdır. Konuyla ilgili çalışma esnasında alan uzmanlarının görüşlerine başvurulmuştur. Elde edilen veriler ışığında toplam 17 kavram haritasından sadece 2 tanesinin hem kavram haritası değerlendirme ölçütlerine hem de materyal tasarlama ilkeleri doğrultusunda bütün maddelere uygun bulunduğu tespit edilmiştir.

Research paper thumbnail of Determinants of Circulant Matrices with Some Certain Sequences

gazi university journal of science, Feb 23, 2015

Let ሼ ሽ be a sequence of real numbers defined by an th order linear homogenous recurrence relatio... more Let ሼ ሽ be a sequence of real numbers defined by an th order linear homogenous recurrence relation. In this paper we obtain a determinant formula for the circulant matrix ൌ ሺ , , ⋯ , ሻ, providing a generalization of determinantal results in papers of Bozkurt [2], Bozkurt and Tam [3], and Shen, et al. [8].

Research paper thumbnail of Millî Eğitim Bakanlığı Eğitim Bilişim Ağı’nda Bulunan Kavram Haritalarının İncelenmesi

Kavram, bir nesnenin zihindeki soyut ve genel tasarimidir. Kavram haritalari zihnin kavramlari da... more Kavram, bir nesnenin zihindeki soyut ve genel tasarimidir. Kavram haritalari zihnin kavramlari daha kolay anlayabilmesi icin tasarlanmis ogrenme araclaridir. Bu calismada Milli Egitim Bakanligi(MEB) Yenilik ve Egitim Teknolojileri Genel Mudurlugu’nun(YEĞITEK) yuruttugu bir proje sonucunda ortaya cikan Egitim Bilisim Agi(EBA) uzerinden yayinlanmis olan kavram haritalari uzerine calisilmistir. Egitim-ogretim surecinde bilisim teknolojisi donanimlarini kullanarak etkin materyaller kullanilmasi amaciyla YEĞITEK tarafindan tasarlanan EBA sinif seviyelerine uygun, guvenilir ve incelemeden gecmis dogru e-icerikleri barindiran sosyal bir platformdur. Arastirma betimsel arastirma yontemlerinden olan dokuman inceleme yoluyla hazirlanmistir. Arastirmanin evrenini EBA’da bulunan Tarih, Kimya, Felsefe, Fen Bilimleri, Arapca ve Turkce alanlarinda hazirlanmis on yedi adet kavram haritasi olusturmaktadir. Arastirmanin amaci EBA’da yayinlanan kavram haritalarinin degerlendirilmesinin yapilmasidir. Konuyla ilgili calisma esnasinda alan uzmanlarinin goruslerine basvurulmustur. Elde edilen veriler isiginda toplam 17 kavram haritasindan sadece 2 tanesinin hem kavram haritasi degerlendirme olcutleri ne hem de materyal tasarlama ilkeleri dogrultusunda butun maddelere uygun bulundugu tespit edilmistir.

Research paper thumbnail of The Bounds for Eigenvalues of Normalized and Signless Laplacian Matrices

arXiv (Cornell University), Aug 25, 2014

In this paper, we obtain the bounds of the extreme eigenvalues of a normalized and signless Lapla... more In this paper, we obtain the bounds of the extreme eigenvalues of a normalized and signless Laplacian matrices using by their traces. In addition, we determine the bounds for k-th eigenvalues of normalized and signless Laplacian matrices.

Research paper thumbnail of Bounds for various graph energies

ITM web of conferences, 2022

In this paper, we obtain some upper and lower bounds for the spectral radius of some special matr... more In this paper, we obtain some upper and lower bounds for the spectral radius of some special matrices such as maximum degree, minimum degree, Randic, sum-connectivity, degree sum, degree square sum, first Zagreb and second Zagreb matrices of a simple connected graph G by the help of matrix theory. We also get some upper bounds for the corresponding energies of G.

Research paper thumbnail of Graphs Associated with Number Sequences

Research paper thumbnail of Lower and Upper Bounds for Some Degree-Based Indices of Graphs

In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced 1... more In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced 1 reciprocal Randic index, Narumi-Katayama index and symmetric division index a graph using solely the 2 vertex degrees. Then we obtain upper and lower bounds for these indices for the complete graphs, path 3 graphs and Fibonacci-sum graphs. Finally, we compared the bounds of these indices for a general graph 4 and some special graphs.

Research paper thumbnail of Bir Grafın GCD Enerjisi İçin Sınırlar

Zenodo (CERN European Organization for Nuclear Research), Nov 30, 2021

Öne Çıkanlar • Bu çalışmada Sayılar Teorisi'nde önemli bir kavram olan GCD (En büyük ortak bölen)... more Öne Çıkanlar • Bu çalışmada Sayılar Teorisi'nde önemli bir kavram olan GCD (En büyük ortak bölen) kavramı Graf Teori'ye taşınarak, grafın derecelerinin en büyük ortak bölenleri kullanılarak bir grafın GCD matrisi tanımlanmıştır. • Tanımlanan grafın GCD matrisinin en büyük özdeğeri (spectral yarıçapı) için alt ve üst sınır verilmiştir. • GCD matrisinin özellikleri göz önüne alınarak bu matrisin enerjisi için bir üst sınır elde edilmiştir. • Bazı özel grafların GCD matrisleri için sonuçlar elde edilmiştir.

Research paper thumbnail of Bir Grafın GCD Spektral Yarıçapı ve GCD Enerjisi İçin Alt ve Üst Sınırlar

Zenodo (CERN European Organization for Nuclear Research), Nov 30, 2021

Öne Çıkanlar • Bir grafın GCD matrisinin en büyük özdeğeri (spectral yarıçapı) için alt ve üst sı... more Öne Çıkanlar • Bir grafın GCD matrisinin en büyük özdeğeri (spectral yarıçapı) için alt ve üst sınır verilmiştir. • GCD matrisinin özellikleri göz önüne alınarak bu matrisin enerjisi için bir üst sınır elde edilmiştir. • Bazı özel grafların GCD matrisleri için sonuçlar elde edilmiştir.