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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 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 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.
