Abstract
The nullity of a graph \(G\), denoted by \(\eta(G)\), 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 \(\eta(G)=n-4\). All known results on trees, unicyclic graphs, bicyclic graphs, graphs with minimum degree 1, and \(r\)-partite graphs, for which \(\eta(G)=n-4\) are shown to be corollaries of a theorem of Chang, Huang and Yeh that characterizes all graphs with nullity \(n-4\).
