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- W1498289380 abstract "The smallest nonzero eigenvalue of the normalized Laplacian matrix of a graph has been extensively studied and shown to have many connections to properties of the graph. We here study a generalization of this eigenvalue, denoted $lambda(G, X)$, introduced by Mendel and Naor in 2010, obtained by embedding the vertices of the graph $G$ into a metric space $X$. We consider general bounds on $lambda(G, X)$ and $lambda(G, H)$, where $H$ is a graph under the standard distance metric, generalizing some existing results for the standard eigenvalue. We consider how $lambda(G, H)$ is affected by changes to $G$ or $H$, and show $lambda(G, H)$ is not monotone in either $G$ or $H$." @default.
- W1498289380 created "2016-06-24" @default.
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- W1498289380 date "2015-01-14" @default.
- W1498289380 modified "2023-09-27" @default.
- W1498289380 title "Bounds on Geometric Eigenvalues of Graphs" @default.
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