Abstract
The Ricci curvature of graphs, as recently introduced by Lin, Lu, and Yau following a general concept due to Ollivier, provides a new and promising isomorphism invariant. This paper presents a simplified exposition of the concept, including the so-called logistic diagram as a computational or visualization aid. Two new infinite classes of graphs with positive Ricci curvature are identified. A local graph-theoretical condition, known as the matching condition, provides a general formula for Ricci curvatures. The paper initiates a longer-term program of classifying the Ricci curvatures of circulant graphs. Aspects of this program may prove useful in tackling the problem of showing when twisted tori are not isomorphic to circulants.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
