Maximum and minimum nullity of a tree degree sequence
classification
🧮 math.CO
keywords
nullitydegreemaximumminimumnumbersequencetreesadjacency
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The nullity of a graph is the multiplicity of the eigenvalue zero in its adjacency spectrum. In this paper, we give a closed formula for the minimum and maximum nullity among trees with the same degree sequence, using the notion of matching number and annihilation number. Algorithms for constructing such minimum-nullity and maximum-nullity trees are described.
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