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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 Fully decentralized and collaborative multilateration primitives for uniquely localizing WSNs(Springer International Publishing AG, 2010) Çakıroğlu, Olca Arda; Erten, CesimWe provide primitives for uniquely localizing WSN nodes. The goal is to maximize the number of uniquely localized nodes assuming a fully decentralized model of computation. Each node constructs a cluster of its own and applies unique localization primitives on it. These primitives are based on constructing a special order for multilaterating the nodes within the cluster. The proposed primitives are fully collaborative and thus the number of iterations required to compute the localization is fewer than that of the conventional iterative multilateration approaches. This further limits the messaging requirements. With relatively small clusters and iteration counts, we can localize almost all the uniquely localizable nodes.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.
