Nut graphs: Maximally extending cores. (English) Zbl 0919.05043

Sciriha, Irene; Gutman, Ivan

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)

MSC:

05C50

Graphs and linear algebra (matrices, eigenvalues, etc.)

Keywords:

nut graph; singular graph; deck of spectra