Semiregular trees with minimal Laplacian spectral radius
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CitationBıyıkoğlu, T. & Leydold, J. (2010). Semiregular trees with minimal laplacian spectral radius. Linear Algebra and its Applications, 432(9), 2335-2341. doi:10.1016/j.laa.2009.06.014
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 examples show that the result cannot be generalized to the class of trees with a given (non-constant) degree sequence.
SourceLinear Algebra and Its Applications