A bound for the permanent of the Laplacian matrix
Copyright policy )A bound for the permanent of the Laplacian matrix
Let L(G) be D-A where D is the diagonal matrix of vertex degrees and A the adjacency matrix. The author proves by an explicit formula that the permanent of L is at least 2(n-1)k where k, the complexity, is the number of spanning trees.
Numerical Analysis, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), Determinants, permanents, traces, other special matrix functions, permanent, Miscellaneous inequalities involving matrices, Discrete Mathematics and Combinatorics, Geometry and Topology, complexity, simple connected graph, Laplacian matrix
Numerical Analysis, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), Determinants, permanents, traces, other special matrix functions, permanent, Miscellaneous inequalities involving matrices, Discrete Mathematics and Combinatorics, Geometry and Topology, complexity, simple connected graph, Laplacian matrix
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