The uniqueness of covers for widely generalized line graphs
Combinatorics
2020-02-20 v1
Abstract
As a natural generalization of line graphs, Hoffman line graphs were defined by Woo and Neumaier. Especially, Hoffman line graphs are closely related to the smallest eigenvalue of graphs, and the uniqueness of strict covers of a Hoffman line graph plays a key role in such a study. In this paper, we prove a theorem for the uniqueness of strict covers under a condition which can be checked in finite time. Our result gives a generalization and a short proof for the main part of [Ars Math.~Contemp. \textbf{1} (2008) 81--98].
Keywords
Cite
@article{arxiv.2002.08049,
title = {The uniqueness of covers for widely generalized line graphs},
author = {Michitaka Furuya and Sho Kubota and Tetsuji Taniguchi and Kiyoto Yoshino},
journal= {arXiv preprint arXiv:2002.08049},
year = {2020}
}