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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 ...
Graphs of given order and size and minimum algebraic connectivity
(Elsevier Science Inc, 2012-04-01)
The 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 ...