English

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.

Keywords

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