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New conjectures on algebraic connectivity and the Laplacian spread of graphs

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arxiv 2201.04225 v1 pith:UA6QFGZ6 submitted 2022-01-11 math.CO

Wayne Barrett , Emily Evans , H. Tracy Hall , Mark Kempton This is my paper · ORCID
classification math.CO
keywords conjecturegraphslaplacianspreadalgebraicboundconjecturesconnectivity
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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.

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