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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 Graphs with given degree sequence and maximal spectral radius(Electronic Journal of Combinatorics, 2008-09-15) Bıyıkoğlu, Türker; Leydold, JosefWe 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 non-increasing with respect to an ordering of the vertices induced by breadth-first search. For trees the resulting structure is uniquely determined up to isomorphism. We also show that the largest spectral radius in such classes of trees is strictly monotone with respect to majorization.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.
