Algebraic connectivity and degree sequences of trees
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CitationBıyıkoğlu, T., & Leydold, J. (2009). Algebraic connectivity and degree sequences of trees. Linear Algebra and its Applications, 430(2), 811-817. doi:10.1016/j.laa.2008.09.030
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 path on non-pendant vertices starting at the characteristic set of the Fiedler vector.