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A NOTE ON NORMALISED HEAT DIFFUSION FOR GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  23 October 2019

BOGDAN NICA Open the ORCID record for BOGDAN NICA [Opens in a new window]
BOGDAN NICA*
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 0G4, Canada email bogdan.nica@mcgill.ca
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Abstract

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We show that, on graphs which have precisely three distinct Laplacian eigenvalues, heat diffusion enjoys a monotonic behaviour.

Keywords

heat kernelLaplacian eigenvalues

MSC classification

Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 1 - 6
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

References

van Dam, E. and Haemers, W. H., ‘Graphs with constant 𝜇 and 𝜇̄’, Discrete Math. 182(1–3) (1998), 293–307; Graph theory, Lake Bled, 1995.CrossRefGoogle Scholar
Godsil, C. D. and McKay, B. D., ‘Feasibility conditions for the existence of walk-regular graphs’, Linear Algebra Appl. 30 (1980), 51–61.CrossRefGoogle Scholar
McMurray Price, T., ‘An inequality for the heat kernel on an Abelian Cayley graph’, Electron. Commun. Probab. 22 (2017), Article ID 57, 8 pages.10.1214/17-ECP84CrossRefGoogle Scholar
Nica, B., A Brief Introduction to Spectral Graph Theory, EMS Textbooks in Mathematics (European Mathematical Society, Zurich, 2018).CrossRefGoogle Scholar
Regev, O. and Shinkar, I., ‘A counterexample to monotonicity of relative mass in random walks’, Electron. Commun. Probab. 21 (2016), Article ID 8, 8 pages.CrossRefGoogle Scholar