New conjectures on algebraic connectivity and the Laplacian spread of graphs
Combinatorics
2022-01-13 v1
Abstract
We conjecture a new lower bound on the algebraic connectivity of a graph that involves the number of vertices of high eccentricity in a graph. We prove that this lower bound implies a strengthening of the Laplacian Spread Conjecture. We discuss further conjectures, also strengthening the Laplacian Spread Conjecture, that include a conjecture for simple graphs and a conjecture for weighted graphs.
Keywords
Cite
@article{arxiv.2201.04225,
title = {New conjectures on algebraic connectivity and the Laplacian spread of graphs},
author = {Wayne Barrett and Emily Evans and H. Tracy Hall and Mark Kempton},
journal= {arXiv preprint arXiv:2201.04225},
year = {2022}
}