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Nut graphs: Maximally extending cores. (English) Zbl 0919.05043
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.
MSC:
05C50Graphs and linear algebra