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Questions related to the field of Combinatorics called Matroid Theory. Relevant topics include matroids in Combinatorial Optimization, Lattice Theory, Algebraic Geometry, Polyhedral Theory, Rigidity, and Algorithms. For questions about Oriented Matroids, the oriented-matroids tag may be used.
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are there pairs of combinatorial graphs that are both isospectral and have the same matroid?
Two graphs are isospectral if the combinatorial Laplacian on them has the same spectrum, equivalently, the adjacency matrix has the same the set of eigenvalues (including multiplicities). Two graphs h …