Optimal embedding and spectral gap of a finite graph
Combinatorics
2020-02-11 v1
Abstract
We introduce a new optimization problem regarding embeddings of a graph into a Euclidean space and discuss its relation to the two, mutually dual, optimizations problems introduced by Goering-Helmberg-Wappler. We prove that the Laplace eigenvalue maximization problem of Goering et al is also dual to our embedding optimization problem. We solve the optimization problems for generalized polygons and graphs isomorphic to the one-skeltons of regular and semi-regular polyhedra.
Cite
@article{arxiv.2002.03584,
title = {Optimal embedding and spectral gap of a finite graph},
author = {Takumi Gomyou and Toshimasa Kobayashi and Takefumi Kondo and Shin Nayatani},
journal= {arXiv preprint arXiv:2002.03584},
year = {2020}
}
Comments
12 pages