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2. 2021/9/28: Detailed references and further reading materials added! 1. Lecture room 2604: 2(15:55-17:30); 4(14:00-15:35). |
Books
[AG] Alexander Grigor'yan, Introduction to Analysis on graphs, University Lecture Series vol. 71, AMS, 2018. Preprint on Prof. Grigor'yan's homepage. [BLS] Türker Bıyıkoğlu, Josef Leydold, Peter F. Stadler, Laplacian Eigenvectors of Graphs, Lecture Notes in Mathematics 1915, Springer, 2007. [DK] Dénes König, Theory of Finite and Infinite Graphs, with a commentary by W. T. Tutte, Birkhäuser, 1990. (originally published in German in 1936 by Akademische Verlagsgesellschaft Leipzig.) [DS] Daniel A. Spielman, Lecture notes of "Graphs and Networks", Fall 2010. [FC] Fan R. K. Chung, Spectral graph theory, CBMS Number 92, AMS, 1997. Revised version on Prof. Chung's homepage [JJ1] Jürgen Jost, Mathematical concepts, Springer, 2015. [JJ2] Jürgen Jost, Mathematical methods in biology and neurobiology, Universitext, Springer, 2014. [KLW] Matthias Keller, Daniel Lenz, Radosław Wojciechowski, Graphs and discrete Dirichlet spaces, GMW 358, Springer, 2021. Preprint on Prof. Keller's homepage. [SY] Richard Schoen, Shing-Tung Yau, Lectures on differential geometry, International Press, 1994. [W07] Radosław Wojciechowski, Stochastic completeness of graphs, PhD Thesis, 2007. arXiv |
Articles
[AL20] F. M. Atay, S. Liu, Cheeger constants, structural balance, and spectral clustering analysis for signed graphs, Discrete Math. 343 (2020), 111616. [BJ13] F. Bauer, J. Jost, Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplacian, Comm. Anal. Geom. 21 (2013), no. 4, 787-845. [CKLP21+] D. Cushing, S. Kamtue, S. Liu, N. Peyerimhoff, Bakry-Émery curvature on graphs as an eigenvalue problem, Calc. Var. accepted, arXiv: 2102.08687. [LLPP15] C. Lange, S. Liu, N. Peyerimhoff, O. Post, Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians, Calc. Var. 54 (2015), 4165-4196. [DGLS01] E. B. Davies, G. M. L. Gladwell, J. Leydold, P. F. Stadler, Discrete nodal domain theorems, Lin. Algebra Appl. 336 (2001), 51-60. [DR94] M. Desai, V. Rao, A characterization of the smallest eigenvalue of a graph, J. Graph Theory 18 (1994), no. 2, 181-194. [Dodziuk83] J. Dodziuk, Maximum principle for parabolic inequalities and the heat flow on open manifolds, Indiana Univ. Math. J. 32 (1983), no. 5, 703-716. [DM06] J. Dodziuk, V. Mathai, Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians, The uniquitous heat kernel, 69-81, Contemp. Math. 398 (2006), AMS, Providence, RI. [Friedman93] J. Friedman, Some geometric aspect of graphs and their eigenfunctions, Duke Math. J. 69 (1993), 485-525. [GKL03] A. Gupta, R. Krauthgamer, J. R. Lee, Bounded geometries, fractals, and low-distortion embeddings, 44th Symposium on Foundations of Computer Sciences (2003), 177-207. [Harary54] F. Harary, On the notion of balance of a signed graph, Michigan Math. J. 2 (1953/54), 143-146. [HL17] B. Hua, Y. Lin, Stochastic completeness for graphs with curvature dimension conditions. Adv. Math. 306 (2017), 279-302. [JL14] J. Jost, S. Liu, Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs, Discrete Comput. Geom. 51 (2014), no. 2, 300-322. [KLLOT13] T.-C. Kwok, L.-C. Lau, Y.-T. Lee, S. Oveis Gharan, L. Trevisan, Improved Cheeger's inequality: Analysis of spectral partitioning algorithms through higher order spectral gap, STOC' 13 (2013), 11-20, ACM, New York. [LOT14] J. R. Lee, S. Oveis Gharan, L. Trevisan, Multiway spectral partitioning and higher-order Cheeger inequalities, J. ACM 61 (2014), no.6, Art. 37, 30pp. [LLMY10] Y. Lin, G. Lippner, D. Mangoubi, S.-T. Yau, Nodal geometry of graphs on surfaces, Discrete Contin. Dyn. Syst. 28 (2010), no. 3, 1291–1298. [LY10] Y. Lin, S.-T. Yau, Ricci curvature and eigenvalue estimate on locally finite graphs, Math. Res. Lett. 17 (2010), no. 2, 343–356. [LMP18] S. Liu, F. Münch, N. Peyerimhoff, Bakry-Émery curvature and diameter bounds on graphs. Calc. Var. 57 (2018), Art. 67. [LMP19] S. Liu, F. Münch, N. Peyerimhoff, Curvature and higher order Buser inequalities for the graph connection Laplacian, SIAM J. Discrete Math. 33 (2019), no.1, 257-305. [LMP17+] S. Liu, F. Münch, N. Peyerimhoff, Rigidity properties of the hypercube via Bakry-Émery curvature, arXiv:1705.06789. [Murty03] M. Ram Murty, Ramanujan graphs, J. Ramanujan Math. Soc. 18 (2003), no.1, 1-20. [Nica20] B. Nica, A note on normalized heat diffusion for graphs, Bull. Aust. Math. Soc. 102 (2020), 1-6. [Nilli91] A. Nilli, On the second eigenvalue of a graph, Discrete Math. 91 (1991), 207-210. [RS12] O. Regev, I. Shinkar, A counterexample to monotonicity of relative mass in random walks, Electron. Commun. Probab. 21 (2016), no. 8, 1-8. [Sch98] M. Schmuckenschläger, Curvature of nonlocal Markov generators, Convex geometric analysis (Berkeley, CA, 1996), 189–197, Math. Sci. Res. Inst. Publ. 34, Cambridge Univ. Press, Cambridge, 1999. [Trevisan12] L. Trevisan, Max cut and the smallest eigenvalue, SIAM J. Comput. 41 (2012), no. 6, 1769-1786. [Weber10] A. Weber, Analysis of the physical Laplacian and the heat flow on a locally fintie graph, J. Math. Anal. Appl. 370 (2010), 146-158. [Youngs63] J. W. T. Youngs, Minimal imbeddings and the genus of a graph, J. Math. Mech. 12 (1963), 303-315. [Zaslavsky10] T. Zaslavsky, Matrices in the theory of signed simple graphs, Ramanujan Math. Soc. Lect. Notes Ser. 13 (2010), 207-229. |