Lorenzo Traldi
Published 2011-01-06, updated 2011-06-26Version 4
We explore the connections between the linear algebra of symmetric matrices over GF(2) and the circuit theory of 4-regular graphs. In particular, we show that the equivalence relation on simple graphs generated by local complementation can also be generated by an operation defined using inverse matrices.
Comments: 22 pages, 5 figures. v2 includes two new results and several minor corrections. v3 includes minor corrections and updated references. v4 has 24 pages and 6 figures; it includes new examples and many modest corrections and revisions. Further revisions may be made before publication in Linear Algebra and its Applications
Well-Quasi-Ordering of Matrices under Schur Complement and Applications to Directed Graphs
Binary matroids and local complementation
One-quasihomomorphisms from the integers into symmetric matrices
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