Abstract
Bakry—Emery theory is used to define a ‘Ricci curvature’ for graphs. An upper bound for the spectral abcissa of the Laplacian of graphs with more than one end is given in terms of this quantity. This is similar to an existing result for manifolds, and the proof of that is also given.
Support was received from NATO Collaborative Research Grants Prog. 0232/87 and the EEC Stimulation Action Plan.
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Elworthy, K.D. (1991). Manifolds and Graphs with Mostly Positive Curvatures. In: Cruzeiro, A.B., Zambrini, J.C. (eds) Stochastic Analysis and Applications. Progress in Probability, vol 26. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0447-3_7
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DOI: https://doi.org/10.1007/978-1-4612-0447-3_7
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