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Yayın Network synchronization: Spectral versus statistical properties(Elsevier B.V., 2006-12) Atay, Fatihcan Mehmet; Bıyıkoğlu, Türker; Jost, JürgenWe 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 inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation and clustering coefficient, can fail to characterize the synchronizability of networks in terms of causal relations, despite the observed correlations.Yayın Dendrimers are the unique chemical trees with maximum spectral radius(Univ Kragujevac, 2012) Bıyıkoğlu, Türker; Leydold, JosefIt is shown that dendrimers have maximum spectral radius and maximum Collatz-Sinogowitz index among all chemical trees of given size. The result is also generalized for the class of chemical trees with prescribed number of pendant vertices.Yayın Algebraic connectivity and degree sequences of trees(Elsevier Science Inc, 2009-01-15) Bıyıkoğlu, Türker; Leydold, JosefWe 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 non-decreasing on every path on non-pendant vertices starting at the characteristic set of the Fiedler vector.Yayın Some notes on spectra of cographs(Charles Babbage Res Ctr, 2011-07) Bıyıkoğlu, Türker; Simic, Slobodan K.; Stanic, ZoranA cograph is a P-4-free 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. As a consequence, we next prove that the polynomial reconstruction of graphs whose vertex-deleted subgraphs have the second largest eigenvalue not exceeding root 5-1/2 is unique.Yayın Largest eigenvalues of the discrete p-Laplacian of trees with degree sequences(Int Linear Algebra Soc, 2009-03) Bıyıkoğlu, Türker; Hellmuth, Marc; Leydold, JosefTrees that have greatest maximum p-Laplacian eigenvalue among all trees with a given degree sequence are characterized. It is shown that such extremal trees can be obtained by breadth-first search where the vertex degrees are non-increasing. These trees are uniquely determined up to isomorphism. Moreover, their structure does not depend on p.
