Trees with maximum nullity

By S. Fiorini, Ivan Gutman, Irene Sciriha. 2005

114 citations recorded by the source corpus.

Abstract The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. Among n -vertex trees, the star has greatest nullity (equal to n − 2). We generalize this by showing that among n -vertex trees whose vertex degrees do not exceed a certain value D , the greatest nullity is n − 2⌈( n − 1)/ D ⌉. Methods for constructing such maximum-nullity trees are described.

Subfields: Electrical and Electronic Engineering, Geometry and Topology, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/b1ae16f814964dba0d94f7d2f66f2ca6709740e1

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In Geometry and Topology

In Organic Chemistry

Citations in the corpus

A characterization of graphs with rank 5 (2012, background): “Motivated by the problem of determining the structural features that force a graph G to be singular, many papers investigated the influence of η(G) (or, equivalently, r(G)) on the structure of the graphG and vice versa (see [3,5,7,17,18,20,24] for examples).”
On the nullity of bicyclic graphs (2005, background): “In [8,9], the nullity of trees and unicyclic graphs are discussed,respectively.”
On the nullity and the matching number of unicyclic graphs (2009, background): “At present, only some particular cases are known [4–6,8–12,14].”
On the nullity of graphs (2007, background): “In recent years, this problem has been investigated by many researchers([5], [7] and [8]).”