[Chaînes fermés et valeurs propres des graphes abélien de Cayley]
Soit
We show that Abelian Cayley graphs contain many closed walks of even length. This implies that given
Accepté le :
Publié le :
Sebastian M. Cioabă 1
@article{CRMATH_2006__342_9_635_0, author = {Sebastian M. Cioab\u{a}}, title = {Closed walks and eigenvalues of {Abelian} {Cayley} graphs}, journal = {Comptes Rendus. Math\'ematique}, pages = {635--638}, publisher = {Elsevier}, volume = {342}, number = {9}, year = {2006}, doi = {10.1016/j.crma.2006.03.005}, language = {en}, }
Sebastian M. Cioabă. Closed walks and eigenvalues of Abelian Cayley graphs. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 635-638. doi : 10.1016/j.crma.2006.03.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.03.005/
[1] Random Cayley graphs and expanders, Random Structures Algorithms, Volume 5 (1994) no. 2, pp. 271-284
[2] S.M. Cioabă, Eigenvalues, expanders and gaps between primes, Ph.D. Thesis, Queen's University at Kingston, Canada, 2005
[3] S.M. Cioabă, On the extreme eigenvalues of regular graphs, Journal of Combinatorial Theory, Series B, in press
[4] Elementary Number Theory, Group Theory and Ramanujan Graphs, Cambridge University Press, 2003
[5] Sums of multinomial coefficients, Canad. Math. Bull., Volume 31 (1988) no. 2, pp. 187-189
[6] Spectral estimates of Abelian Cayley graphs, Journal of Combinatorial Theory, Series B, Volume 96 (2006) no. 1, pp. 111-121
[7] Ramanujan graphs, Combinatorica, Volume 8 (1988) no. 3, pp. 261-277
[8] Tight estimates for eigenvalues of regular graphs, Electron. J. Combin., Volume 11 (2004) no. 9, pp. 1-4
[9] Character sums and Abelian Ramanujan graphs, J. Number Theory, Volume 41 (1992), pp. 199-217
- Eigenvalues of Cayley graphs, The Electronic Journal of Combinatorics, Volume 29 (2022) no. 2, p. research | Zbl:1492.05093
- Spectral properties of Cayley graphs of split metacyclic groups, Journal of the Ramanujan Mathematical Society, Volume 35 (2020) no. 2, pp. 159-175 | Zbl:7268671
- , 2017 IEEE 37th International Conference on Distributed Computing Systems Workshops (ICDCSW) (2017), p. 175 | DOI:10.1109/icdcsw.2017.71
- On the spectrum of the generalised Petersen graphs, Graphs and Combinatorics, Volume 32 (2016) no. 5, pp. 1843-1850 | DOI:10.1007/s00373-016-1676-0 | Zbl:1351.05141
- The spectrum and toughness of regular graphs, Discrete Applied Mathematics, Volume 176 (2014), pp. 43-52 | DOI:10.1016/j.dam.2013.12.004 | Zbl:1298.05200
- Cryptography, Handbook of Finite Fields (2013), p. 777 | DOI:10.1201/b15006-22
- The Combinatorial Trace Method in Action, The College Mathematics Journal, Volume 44 (2013) no. 1, p. 32 | DOI:10.4169/college.math.j.44.1.032
- Nonexistence of a circulant expander family, Bulletin of the Australian Mathematical Society, Volume 83 (2011) no. 1, pp. 87-95 | DOI:10.1017/s0004972710001644 | Zbl:1213.05170
- Matchings in regular graphs from eigenvalues, Journal of Combinatorial Theory. Series B, Volume 99 (2009) no. 2, pp. 287-297 | DOI:10.1016/j.jctb.2008.06.008 | Zbl:1205.05177
Cité par 9 documents. Sources : Crossref, zbMATH
Commentaires - Politique