Optimal embedding and spectral gap of a finite graph

Autor:	Gomyou, Takumi, Kobayashi, Toshimasa, Kondo, Takefumi, Nayatani, Shin
Rok vydání:	2020
Předmět:	Mathematics - Combinatorics 05C62 (Primary) 05C50 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 12 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2002.03584 Zobrazit plný text záznamu View this record from Arxiv