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arXiv:2201.04225 [math.CO]AbstractReferencesReviewsResources

New conjectures on algebraic connectivity and the Laplacian spread of graphs

Wayne Barrett, Emily Evans, H. Tracy Hall, Mark Kempton

Published 2022-01-11Version 1

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.

Categories: math.CO
Subjects: 05C50
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