Trees with maximum nullity
Copyright policy )Trees with maximum nullity
The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. Among all \(n\)-vertex trees, the star tree has greatest nullity (equal to \(n-2\)). In this paper it is shown that among all \(n\)-vertex trees whose vertex degrees do not exceed a fixed value \(D\), the greatest nullity is \(n- 2 \lceil (n-1)/D \rceil\). In addition, methods for constructing some such greatest nullity trees are presented, together with a conjectured description of these trees.
- University of Malta Malta
- University of Kragujevac Serbia
- University of Kragujevac, Faculty of Science Serbia
Eigenvalues (of graphs), Maximum-nullity trees, Numerical Analysis, Algebra and Number Theory, Maximal matchings, Graphs and linear algebra (matrices, eigenvalues, etc.), eigenvalues, Independent edges, Trees, Discrete Mathematics and Combinatorics, Geometry and Topology, Nullity, maximal matchings
Eigenvalues (of graphs), Maximum-nullity trees, Numerical Analysis, Algebra and Number Theory, Maximal matchings, Graphs and linear algebra (matrices, eigenvalues, etc.), eigenvalues, Independent edges, Trees, Discrete Mathematics and Combinatorics, Geometry and Topology, Nullity, maximal matchings
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