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A characterization of singular graphs. (English) Zbl 1142.05344
Summary: Characterization of singular graphs can be reduced to the non-trivial solutions of a system of linear homogeneous equations 𝐀𝐱=0 for the 0-1 adjacency matrix 𝐀. A graph G is singular of nullity η(G) greater than or equal to 1, if the dimension of the nullspace ker(𝐀) of its adjacency matrix A is η(G). Necessary and sufficient conditions are determined for a graph to be singular in terms of admissible induced subgraphs.
MSC:
05C50Graphs and linear algebra