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New conjectures on algebraic connectivity and the Laplacian spread of graphs

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  • NSTL
  • Elsevier
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. (c) 2022 Elsevier Inc. All rights reserved.

LaplacianEigenvalueLaplacian spread conjectureAlgebraic connectivityEccentricity

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

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Brigham Young Univ

Hall Labs LLC

2022

10.1016/j.laa.2022.04.021

Linear Algebra and its Applications

Linear Algebra and its Applications

EISCI
ISSN：0024-3795
年,卷(期)：2022.648
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