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Algebraic connectivity and degree sequences of trees
(Elsevier Science Inc, 2009-01-15)
We 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 ...
Semiregular trees with minimal Laplacian spectral radius
(Elsevier Inc, 2010-04-15)
A 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 ...