Browsing FEF  Makale Koleksiyonu  Matematik Bölümü / Department of Mathematics by Author "Bıyıkoğlu, Türker"
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Algebraic connectivity and degree sequences of trees
Bıyıkoğlu, Türker; Leydold, Josef (Elsevier Science Inc, 20090115)We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are nondecreasing on every ... 
Cryptanalysis of Fridrich's chaotic image encryption
Solak, Ercan; Çokal, Cahit; Yıldız, Olcay Taner; Bıyıkoğlu, Türker (World Scientific Publishing, 201005)We cryptanalyze Fridrich's chaotic image encryption algorithm. We show that the algebraic weaknesses of the algorithm make it vulnerable against chosenciphertext attacks. We propose an attack that reveals the secret ... 
Dendrimers are the unique chemical trees with maximum spectral radius
Bıyıkoğlu, Türker; Leydold, Josef (Univ Kragujevac, 2012)It is shown that dendrimers have maximum spectral radius and maximum CollatzSinogowitz index among all chemical trees of given size. The result is also generalized for the class of chemical trees with prescribed number ... 
Discovering cisregulatory modules by optimizing barbecues
Mosig, Axel; Bıyıkoğlu, Türker; Prohaska, Sonja J.; Stadler, Peter F. (Elsevier Science Bv, 20090528)Gene expression in eukaryotic cells is regulated by a complex network of interactions, in which transcription factors and their binding sites on the genomic DNA play a determining role. As transcription factors rarely, if ... 
Fourcycled graphs with topological applications
Bıyıkoğlu, Türker; Civan, Yusuf (Birkhauser Verlag AG, 201203)We call a simple graph G a 4cycled graph if either it has no edges or every edge of it is contained in an induced 4cycle of G. Our interest on 4cycled graphs is motivated by the fact that their clique complexes play an ... 
Geometric representations and symmetries of graphs, maps and other discrete structures and applications in science
Bıyıkoğlu, Türker; Özkahya, Lale (Tübitak, 201509)Bu proje çalışmasının birinci amacı çizgelerin özdeğer ve özvektör yapılarını çizge özellik ve sabitleri ile ilişkilendirmektir. İkinci amacı biyoloji, bioinformatik, dinamik sistemler, haberleşme, kriptoloji ve sosyal ... 
Graphs of given order and size and minimum algebraic connectivity
Bıyıkoğlu, Türker; Leydold, Josef (Elsevier Science Inc, 20120401)The structure of connected graphs of given size and order that have minimal algebraic connectivity is investigated. It is shown that they must consist of a chain of cliques. Moreover, an upper bound for the number of maximal ... 
Graphs with given degree sequence and maximal spectral radius
Bıyıkoğlu, Türker; Leydold, Josef (Electronic Journal of Combinatorics, 20080915)We describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is nonincreasing with respect ... 
Laplacian Eigenvectors of graphs
Bıyıkoğlu, Türker; Leydold, Josef; Stadler, Peter F. (Springer Verlag, 2007)[No abstract available] 
Largest eigenvalues of the discrete pLaplacian of trees with degree sequences
Bıyıkoğlu, Türker; Hellmuth, Marc; Leydold, Josef (Int Linear Algebra Soc, 200903)Trees that have greatest maximum pLaplacian eigenvalue among all trees with a given degree sequence are characterized. It is shown that such extremal trees can be obtained by breadthfirst search where the vertex degrees ... 
Network synchronization: Spectral versus statistical properties
Atay, Fatihcan Mehmet; Bıyıkoğlu, Türker; Jost, Jürgen (Elsevier B.V., 200612)We consider synchronization of weighted networks, possibly with asymmetrical connections. Focusing on causal relations rather than the observed correlations, we show that the synchronizability of networks cannot be directly ... 
Semiregular trees with minimal Laplacian spectral radius
Bıyıkoğlu, Türker; Leydold, Josef (Elsevier Inc, 20100415)A semiregular tree is a tree where all nonpendant vertices have the same degree. Among all semiregular trees with fixed order and degree, a graph with minimal (adjacency/Laplacian) spectral radius is a caterpillar. Counter ... 
Some notes on spectra of cographs
Bıyıkoğlu, Türker; Simic, Slobodan K.; Stanic, Zoran (Charles Babbage Res Ctr, 201107)A cograph is a P4free graph. We first give a short proof of the fact that 0 (1) belongs to the spectrum of a connected cograph (with at least two vertices) if and only if it contains duplicate (resp. coduplicate) vertices. ...