Ramanujan graph (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Ramanujan graph" in English language version.

refsWebsite

Global rank English rank

11doi.org

2^nd place

7arxiv.org

69^th place

59^th place

4semanticscholar.org

11^th place

8^th place

4ams.org

451^st place

277^th place

2worldcat.org

5^th place

2nih.gov

4^th place

1queensu.ca

6,111^th place

3,868^th place

1wolfram.com

513^th place

537^th place

1harvard.edu

18^th place

17^th place

1mathnet.ru

8,783^rd place

low place

1princeton.edu

741^st place

577^th place

1yale.edu

565^th place

460^th place

1projecteuclid.org

3,707^th place

2,409^th place

1quantamagazine.org

6,413^th place

4,268^th place

1iacr.org

5,032^nd place

3,357^th place

1bham.ac.uk

6,934^th place

4,192^nd place

ams.org

mathscinet.ams.org

Terras, Audrey (2011), Zeta functions of graphs: A stroll through the garden, Cambridge Studies in Advanced Mathematics, vol. 128, Cambridge University Press, ISBN 978-0-521-11367-0, MR 2768284
Pizer, Arnold K. (1990), "Ramanujan graphs and Hecke operators", Bulletin of the American Mathematical Society, New Series, 23 (1): 127–137, doi:10.1090/S0273-0979-1990-15918-X, MR 1027904
Friedman, Joel (2003). "Relative expanders or weakly relatively Ramanujan graphs". Duke Mathematical Journal. 118 (1): 19–35. doi:10.1215/S0012-7094-03-11812-8. MR 1978881.
Eisenträger, Kirsten; Hallgren, Sean; Lauter, Kristin; Morrison, Travis; Petit, Christophe (2018), "Supersingular isogeny graphs and endomorphism rings: Reductions and solutions" (PDF), in Nielsen, Jesper Buus; Rijmen, Vincent (eds.), Advances in Cryptology – EUROCRYPT 2018: 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tel Aviv, Israel, April 29 - May 3, 2018, Proceedings, Part III (PDF), Lecture Notes in Computer Science, vol. 10822, Cham: Springer, pp. 329–368, doi:10.1007/978-3-319-78372-7_11, ISBN 978-3-319-78371-0, MR 3794837, S2CID 4850644

arxiv.org

Michael B. Cohen (2016). Ramanujan Graphs in Polynomial Time. Foundations of Computer Science (FOCS), 2016 IEEE 57th Annual Symposium. arXiv:1604.03544. doi:10.1109/FOCS.2016.37.
Hall, Chris; Puder, Doron; Sawin, William F. (2018). "Ramanujan coverings of graphs". Advances in Mathematics. 323: 367–410. arXiv:1506.02335. doi:10.1016/j.aim.2017.10.042.
Miller, Steven J.; Novikoff, Tim; Sabelli, Anthony (2008). "The Distribution of the Largest Non-trivial Eigenvalues in Families of Random Regular Graphs". Experimental Mathematics. 17 (2): 231–244. arXiv:math/0611649. doi:10.1080/10586458.2008.10129029.
Huang, Jiaoyang; McKenzie, Theo; Yau, Horng-Tzer (2024). "Ramanujan Property and Edge Universality of Random Regular Graphs". arXiv:2412.20263 [math.PR].
Lee, Yin Tat; Peng, Richard; Spielman, Daniel A. (2015-08-13). "Sparsified Cholesky Solvers for SDD linear systems". arXiv:1506.08204 [cs.DS].
Lubetzky, Eyal; Peres, Yuval (2016-07-01). "Cutoff on all Ramanujan graphs". Geometric and Functional Analysis. 26 (4): 1190–1216. arXiv:1507.04725. doi:10.1007/s00039-016-0382-7. ISSN 1420-8970. S2CID 13803649.
Lubetzky, Eyal; Sly, Allan (2011-01-01). "Explicit Expanders with Cutoff Phenomena". Electronic Journal of Probability. 16 (none). arXiv:1003.3515. doi:10.1214/EJP.v16-869. ISSN 1083-6489. S2CID 9121682.

bham.ac.uk

pure-oai.bham.ac.uk

Eisenträger, Kirsten; Hallgren, Sean; Lauter, Kristin; Morrison, Travis; Petit, Christophe (2018), "Supersingular isogeny graphs and endomorphism rings: Reductions and solutions" (PDF), in Nielsen, Jesper Buus; Rijmen, Vincent (eds.), Advances in Cryptology – EUROCRYPT 2018: 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tel Aviv, Israel, April 29 - May 3, 2018, Proceedings, Part III (PDF), Lecture Notes in Computer Science, vol. 10822, Cham: Springer, pp. 329–368, doi:10.1007/978-3-319-78372-7_11, ISBN 978-3-319-78371-0, MR 3794837, S2CID 4850644

doi.org

Alexander Lubotzky; Ralph Phillips; Peter Sarnak (1988). "Ramanujan graphs". Combinatorica. 8 (3): 261–277. doi:10.1007/BF02126799. S2CID 206812625.
Li, Winnie (2020). "The Ramanujan conjecture and its applications". Philosophical Transactions of the Royal Society A. 378–2163 (2163). Bibcode:2020RSPTA.37880441W. doi:10.1098/rsta.2018.0441. PMC 6939229. PMID 31813366.
Moshe Morgenstern (1994). "Existence and Explicit Constructions of q+1 Regular Ramanujan Graphs for Every Prime Power q". Journal of Combinatorial Theory. Series B. 62: 44–62. doi:10.1006/jctb.1994.1054.
Pizer, Arnold K. (1990), "Ramanujan graphs and Hecke operators", Bulletin of the American Mathematical Society, New Series, 23 (1): 127–137, doi:10.1090/S0273-0979-1990-15918-X, MR 1027904
Michael B. Cohen (2016). Ramanujan Graphs in Polynomial Time. Foundations of Computer Science (FOCS), 2016 IEEE 57th Annual Symposium. arXiv:1604.03544. doi:10.1109/FOCS.2016.37.
Hall, Chris; Puder, Doron; Sawin, William F. (2018). "Ramanujan coverings of graphs". Advances in Mathematics. 323: 367–410. arXiv:1506.02335. doi:10.1016/j.aim.2017.10.042.
Friedman, Joel (2003). "Relative expanders or weakly relatively Ramanujan graphs". Duke Mathematical Journal. 118 (1): 19–35. doi:10.1215/S0012-7094-03-11812-8. MR 1978881.
Miller, Steven J.; Novikoff, Tim; Sabelli, Anthony (2008). "The Distribution of the Largest Non-trivial Eigenvalues in Families of Random Regular Graphs". Experimental Mathematics. 17 (2): 231–244. arXiv:math/0611649. doi:10.1080/10586458.2008.10129029.
Lubetzky, Eyal; Peres, Yuval (2016-07-01). "Cutoff on all Ramanujan graphs". Geometric and Functional Analysis. 26 (4): 1190–1216. arXiv:1507.04725. doi:10.1007/s00039-016-0382-7. ISSN 1420-8970. S2CID 13803649.
Lubetzky, Eyal; Sly, Allan (2011-01-01). "Explicit Expanders with Cutoff Phenomena". Electronic Journal of Probability. 16 (none). arXiv:1003.3515. doi:10.1214/EJP.v16-869. ISSN 1083-6489. S2CID 9121682.
Eisenträger, Kirsten; Hallgren, Sean; Lauter, Kristin; Morrison, Travis; Petit, Christophe (2018), "Supersingular isogeny graphs and endomorphism rings: Reductions and solutions" (PDF), in Nielsen, Jesper Buus; Rijmen, Vincent (eds.), Advances in Cryptology – EUROCRYPT 2018: 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tel Aviv, Israel, April 29 - May 3, 2018, Proceedings, Part III (PDF), Lecture Notes in Computer Science, vol. 10822, Cham: Springer, pp. 329–368, doi:10.1007/978-3-319-78372-7_11, ISBN 978-3-319-78371-0, MR 3794837, S2CID 4850644

harvard.edu

ui.adsabs.harvard.edu

Li, Winnie (2020). "The Ramanujan conjecture and its applications". Philosophical Transactions of the Royal Society A. 378–2163 (2163). Bibcode:2020RSPTA.37880441W. doi:10.1098/rsta.2018.0441. PMC 6939229. PMID 31813366.

iacr.org

eprint.iacr.org

Eisenträger, Kirsten; Hallgren, Sean; Lauter, Kristin; Morrison, Travis; Petit, Christophe (2018), "Supersingular isogeny graphs and endomorphism rings: Reductions and solutions" (PDF), in Nielsen, Jesper Buus; Rijmen, Vincent (eds.), Advances in Cryptology – EUROCRYPT 2018: 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tel Aviv, Israel, April 29 - May 3, 2018, Proceedings, Part III (PDF), Lecture Notes in Computer Science, vol. 10822, Cham: Springer, pp. 329–368, doi:10.1007/978-3-319-78372-7_11, ISBN 978-3-319-78371-0, MR 3794837, S2CID 4850644

mathnet.ru

Margulis, G. A. (1988). "Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators". Probl. Peredachi Inf. 24–1: 51–60.

nih.gov

ncbi.nlm.nih.gov

Li, Winnie (2020). "The Ramanujan conjecture and its applications". Philosophical Transactions of the Royal Society A. 378–2163 (2163). Bibcode:2020RSPTA.37880441W. doi:10.1098/rsta.2018.0441. PMC 6939229. PMID 31813366.

pubmed.ncbi.nlm.nih.gov

Li, Winnie (2020). "The Ramanujan conjecture and its applications". Philosophical Transactions of the Royal Society A. 378–2163 (2163). Bibcode:2020RSPTA.37880441W. doi:10.1098/rsta.2018.0441. PMC 6939229. PMID 31813366.

princeton.edu

annals.math.princeton.edu

Adam Marcus; Daniel Spielman; Nikhil Srivastava (2013). Interlacing families I: Bipartite Ramanujan graphs of all degrees (PDF). Foundations of Computer Science (FOCS), 2013 IEEE 54th Annual Symposium.

projecteuclid.org

Miller, Steven J.; Novikoff, Tim; Sabelli, Anthony (2008). "The Distribution of the Largest Non-trivial Eigenvalues in Families of Random Regular Graphs". Experimental Mathematics. 17 (2): 231–244. arXiv:math/0611649. doi:10.1080/10586458.2008.10129029.

quantamagazine.org

Sloman, Leila (2025-04-18). "New Proof Settles Decades-Old Bet About Connected Networks". Quanta Magazine. Retrieved 2025-05-06.

queensu.ca

mast.queensu.ca

Survey paper by M. Ram Murty

semanticscholar.org

api.semanticscholar.org

Alexander Lubotzky; Ralph Phillips; Peter Sarnak (1988). "Ramanujan graphs". Combinatorica. 8 (3): 261–277. doi:10.1007/BF02126799. S2CID 206812625.
Lubetzky, Eyal; Peres, Yuval (2016-07-01). "Cutoff on all Ramanujan graphs". Geometric and Functional Analysis. 26 (4): 1190–1216. arXiv:1507.04725. doi:10.1007/s00039-016-0382-7. ISSN 1420-8970. S2CID 13803649.
Lubetzky, Eyal; Sly, Allan (2011-01-01). "Explicit Expanders with Cutoff Phenomena". Electronic Journal of Probability. 16 (none). arXiv:1003.3515. doi:10.1214/EJP.v16-869. ISSN 1083-6489. S2CID 9121682.
Eisenträger, Kirsten; Hallgren, Sean; Lauter, Kristin; Morrison, Travis; Petit, Christophe (2018), "Supersingular isogeny graphs and endomorphism rings: Reductions and solutions" (PDF), in Nielsen, Jesper Buus; Rijmen, Vincent (eds.), Advances in Cryptology – EUROCRYPT 2018: 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tel Aviv, Israel, April 29 - May 3, 2018, Proceedings, Part III (PDF), Lecture Notes in Computer Science, vol. 10822, Cham: Springer, pp. 329–368, doi:10.1007/978-3-319-78372-7_11, ISBN 978-3-319-78371-0, MR 3794837, S2CID 4850644

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Icosahedral Graph". mathworld.wolfram.com. Retrieved 2019-11-29.

worldcat.org

search.worldcat.org

Lubetzky, Eyal; Peres, Yuval (2016-07-01). "Cutoff on all Ramanujan graphs". Geometric and Functional Analysis. 26 (4): 1190–1216. arXiv:1507.04725. doi:10.1007/s00039-016-0382-7. ISSN 1420-8970. S2CID 13803649.
Lubetzky, Eyal; Sly, Allan (2011-01-01). "Explicit Expanders with Cutoff Phenomena". Electronic Journal of Probability. 16 (none). arXiv:1003.3515. doi:10.1214/EJP.v16-869. ISSN 1083-6489. S2CID 9121682.

yale.edu

cs.yale.edu

Adam Marcus; Daniel Spielman; Nikhil Srivastava (2015). Interlacing families IV: Bipartite Ramanujan graphs of all sizes (PDF). Foundations of Computer Science (FOCS), 2015 IEEE 56th Annual Symposium.