Sciriha, Irene; Gutman, Ivan Nut graphs: Maximally extending cores. (English) Zbl 0919.05043 Util. Math. 54, 257-272 (1998). A graph is a nut graph if its adjacency matrix has nullity one and all the components of a non-zero eigenvector corresponding to the eigenvalue zero are non-zero. Nut graphs are shown to be connected and non-bipartite and to exist for any order greater than or equal to seven. From the main result, namely that a nut graph has a deck of non-singular vertex deleted subgraphs, more structural features are deduced. Reviewer: Brigitte Servatius (Worcester) Cited in 10 Documents MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) Keywords:nut graph; singular graph; deck of spectra PDF BibTeX XML Cite \textit{I. Sciriha} and \textit{I. Gutman}, Util. Math. 54, 257--272 (1998; Zbl 0919.05043)