On some extremal problems in graph theory
Combinatorics
2007-05-23 v1 Mathematical Physics
math.MP
Rings and Algebras
Spectral Theory
Abstract
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.
Cite
@article{arxiv.math/9907050,
title = {On some extremal problems in graph theory},
author = {Dmitry Jakobson and Igor Rivin},
journal= {arXiv preprint arXiv:math/9907050},
year = {2007}
}
Comments
June 1998 Preprint