Extremal metrics on graphs I
Copyright policy )Extremal metrics on graphs I
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants (girth, diameter), and spectral invariants (the determinant of the Laplace operator, or complexity; bottom non-zero eigenvalue of the Laplace operator). We show that almost all of these functions are, surprisingly, convex, and we characterize the valuations extremizing these invariant
16 pages
Extremal problems in graph theory, Distance in graphs, Graphs and linear algebra (matrices, eigenvalues, etc.), metrics on graphs, metric invariants, 90C35, 05C35;05C85;49K35;90C35, Laplace operator, spectral invariants, FOS: Mathematics, eigenvalue, Mathematics - Combinatorics, 05C85, 49K35, Combinatorics (math.CO), 05C35
Extremal problems in graph theory, Distance in graphs, Graphs and linear algebra (matrices, eigenvalues, etc.), metrics on graphs, metric invariants, 90C35, 05C35;05C85;49K35;90C35, Laplace operator, spectral invariants, FOS: Mathematics, eigenvalue, Mathematics - Combinatorics, 05C85, 49K35, Combinatorics (math.CO), 05C35
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