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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 Graphs of given order and size and minimum algebraic connectivity(Elsevier Science Inc, 2012-04-01) Bıyıkoğlu, Türker; Leydold, JosefThe 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 cliques of size 2 or larger is derived.Yayın Semiregular trees with minimal Laplacian spectral radius(Elsevier Inc, 2010-04-15) Bıyıkoğlu, Türker; Leydold, JosefA semiregular tree is a tree where all non-pendant 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 examples show that the result cannot be generalized to the class of trees with a given (non-constant) degree sequence.
