Characterizing Graphs with Nullity n−4

Document Type

Article

Publication Title

Match

Abstract

The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in the spectrum of G. A unified approach is presented for the characterization of graphs of order n with η(G) = n − 4. All known results on trees, unicyclic graphs, bicyclic graphs, graphs with minimum degree 1, and r-partite graphs, for which η(G) = n − 4 are shown to be corollaries of a theorem of Chang, Huang and Yeh that characterizes all graphs with nullity n − 4.

First Page

631

Last Page

642

DOI

10.46793/match.89-3.631P

Publication Date

1-1-2023

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