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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 ...
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 ...