On some extremal problems in graph theory

Details On some extremal problems in graph theory On some extremal problems in graph theory

1999-07-08

arxiv.org/abs/math/9907050v1

Mathematics

Combinatorics

June 1998 Preprint

Scientific paper

In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs -- weighing the graph changes a combinatorial problem to one in analysis. We study both weighted and unweighted graphs which are extremal for these invariants. In the unweighted case we concentrate on finding extrema among all (usually) regular graphs with the same number of vertices; we also study the relationships between such graphs.

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