The johnson graph
Rodolfo Conde
Hi everyone...
Does anyone know of some good papers about the johnson graph ?? This
graph has as vertex set all m-subset of {1, ..., n } and two vertices
s1, s2 are adjacent if and only if |s1 \cap s2 | = m - 1. I have searhed
over the internet but i can only find litte information about this graph
Thanks everyone for your help
Cheers...
Gerry Myerson
Rodolfo Conde <r...@gmx.co.uk> wrote:
> Hi everyone...
>
> Does anyone know of some good papers about the johnson graph ?? This
> graph has as vertex set all m-subset of {1, ..., n } and two vertices
> s1, s2 are adjacent if and only if |s1 \cap s2 | = m - 1. I have searhed
> over the internet but i can only find litte information about this graph
Do you have access to Math Reviews online?
A search there for johnson graph turned up 72 results.
Here are the first 20.
MR2656274 Ning, Wantao; Li, Qiuli; Zhang, Heping Smallest generalized
cuts and diameter-increasing sets of Johnson graphs. Ars Combin. 95
(2010), 353--362. 05C40 (05C12)
MR2590755 Mogil?nykh, I. Yu. On the nonexistence of some perfect
2-colorings of Johnson graphs. (Russian) Diskretn. Anal. Issled. Oper.
16 (2009), no. 5, 52--68, 92--93. 05C15
MR2423342 (2009e:05247) Devillers, Alice; Giudici, Michael; Li, Cai
Heng; Praeger, Cheryl E. Primitive decompositions of Johnson graphs. J.
Combin. Theory Ser. A 115 (2008), no. 6, 925--966. (Reviewer: Giuseppe
Mazzuoccolo) 05C70 (05C25)
MR2390366 (2008m:05306) Krebs, Mike; Shaheen, Anthony On the spectra of
Johnson graphs. Electron. J. Linear Algebra 17 (2008), 154--167.
(Reviewer: Antonio Pasini) 05E10 (05C50 20C30 43A90)
MR2388373 (2009b:05271) Wang, Kaishun; Li, Zengti Lattices associated
with distance-regular graphs. European J. Combin. 29 (2008), no. 2,
379--385. (Reviewer: Jaume Pujol) 05E30 (05B35 06A07)
MR2372841 (2008j:05163) Cuaresma, Maria Cristeta; Giudici, Michael;
Praeger, Cheryl E. Homogeneous factorisations of Johnson graphs. Des.
Codes Cryptogr. 46 (2008), no. 3, 303--327. (Reviewer: Marston Conder)
05C25 (05C70 20B25)
MR2368026 (2008j:05119) Vallentin, Frank Optimal distortion embeddings
of distance regular graphs into Euclidean spaces. J. Combin. Theory Ser.
B 98 (2008), no. 1, 95--104. (Reviewer: Joel Foisy) 05C10 (05C85 05E30
57M15 68R10)
MR2406142 (2009e:05122) Mogil?nykh, I. Yu. On the regularity of perfect
colorings of the Johnson graph in two colors. (Russian) Problemy
Peredachi Informatsii 43 (2007), no. 4, 37--44; translation in Probl.
Inf. Transm. 43 (2007), no. 4, 303--309 (Reviewer: Peter Mihók) 05C15
(94B25)
MR2338247 (2008h:05102) Paduchikh, D. V. The nonexistence of locally
$\overline{J}(10,5)$-graphs. Proc. Steklov Inst. Math. 257 (2007),
suppl. 1, S155--S163. (Reviewer: Robert Beezer) 05C75 (05E30)
MR2339488 (2008i:05049) Du, Shao-Fei; Jones, Gareth; Kwak, Jin Ho;
Nedela, Roman; ?koviera, Martin Regular embeddings of $K_{n,n}$ where
$n$ is a power of 2. I. Metacyclic case. European J. Combin. 28 (2007),
no. 6, 1595--1609. (Reviewer: Aleksander Malni?) 05C10 (05C25 20B25)
MR2316893 (2008m:81102) Hora, Akihito; Obata, Nobuaki Quantum
probability and spectral analysis of graphs. With a foreword by Luigi
Accardi. Theoretical and Mathematical Physics. Springer, Berlin, 2007.
xviii+371 pp. ISBN: 978-3-540-48862-0 (Reviewer: Uwe Franz) 81S25 (05C50
20C30 20P05 46L60 60F05 81-02)
MR2287449 (2008d:05165) Bang, S.; Hiraki, A.; Koolen, J. H. Delsarte
clique graphs. European J. Combin. 28 (2007), no. 2, 501--516.
(Reviewer: Willem H. Haemers) 05E30 (05C50 05C69)
MR2269558 (2008f:05210) van Dam, E. R.; Haemers, W. H.; Koolen, J. H.;
Spence, E. Characterizing distance-regularity of graphs by the spectrum.
J. Combin. Theory Ser. A 113 (2006), no. 8, 1805--1820. 05E30 (05C50)
MR2231096 (2007b:05216) Tanaka, Hajime Classification of subsets with
minimal width and dual width in Grassmann, bilinear forms and dual polar
graphs. J. Combin. Theory Ser. A 113 (2006), no. 5, 903--910. (Reviewer:
Guan Tie Deng) 05E30
MR2220250 (2007b:05142) Levenshtein, Vladimir I. New problems of graph
reconstruction. Bayreuth. Math. Schr. No. 74 (2005), 239--255.
(Reviewer: Mark N. Ellingham) 05C60 (94B99)
MR2116180 (2006f:05088) Jones, Gareth A. Automorphisms and regular
embeddings of merged Johnson graphs. European J. Combin. 26 (2005), no.
3-4, 417--435. (Reviewer: Robert Jajcay) 05C25 (05C10)
MR2065909 (2005a:05172) Pizaña, Miguel A. Distances and diameters on
iterated clique graphs. Discrete Appl. Math. 141 (2004), no. 1-3,
255--261. 05C69 (05C12)
MR2062187 (2005i:82032) Hora, Akihito Asymptotic spectral analysis on
the Johnson graphs in infinite degree and zero temperature limit. The
Proceedings of the Second Sendai Workshop on Quantum Probability and
Quantum Information. Interdiscip. Inform. Sci. 10 (2004), no. 1, 1--10.
(Reviewer: Zhong Gen Su) 82B41 (60F05)
MR2003920 (2004i:81131) Hora, Akihito; Obata, Nobuaki Quantum
decomposition and quantum central limit theorem. Fundamental aspects of
quantum physics (Tokyo, 2001), 284--305, QP--PQ: Quantum Probab. White
Noise Anal., 17, World Sci. Publ., River Edge, NJ, 2003. (Reviewer:
Alexei Zhedanov) 81S25 (33C45)
MR2002619 (2004k:05211) Juri?i?, Aleksandar; Koolen, Jack 1-homogeneous
graphs with cocktail party $µ$-graphs. J. Algebraic Combin. 18 (2003),
no. 2, 79--98. (Reviewer: Willem H. Haemers) 05E30
--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)