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Bilinear matrix equation characterizes Laplacian and distance matrices of weighted trees
Mikhail Goubko, Alexander Veremyev
It is known from the algebraic graph theory that if is the Laplacian matrix of some tree with a vertex degree sequence and is its dist…
Lower bound for the cost of connecting tree with given vertex degree sequence
Mikhail Goubko, Alexander Kuznetsov
The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, g…
Maximizing Wiener Index for Trees with Given Vertex Weight and Degree Sequences
Mikhail Goubko
The Wiener index is maximized over the set of trees with the given vertex weight and degree sequences. This model covers the traditional "unweighed" Wiener index, the terminal Wien…
On Minimum Terminal Distance Spectral Radius of Trees with Given Degree Sequence
Mikhail Goubko
For a tree with the given sequence of vertex degrees the spectral radius of its terminal distance matrix is shown to be bounded from below by the the average row sum of the termina…