References on Cages

This page contains a list of references regarding (k,g)-cages, which are k-regular graphs of girth g with the fewest possible number of vertices. This collection of references is the joint reference list for the two pages

References

Each reference is accompanied by a direct link to its review in Math Reviews (if it has one). These will not work unless your institution has a subscription to online Math Reviews.

[Bal73] 48#5916: A.T. Balaban,
Trivalent graphs of girth nine and eleven and relationships among the cages,
Rev. Roumaine Math 18, 1973, 1033-1043.
[BiH 80] 81e:05112: N.L. Biggs and M.J. Hoare,
A trivalent graph with 58 vertices and girth 9,
Discrete Math 30, 1980, 299-301.
[BiH 83] 85a:05038: N.L. Biggs and M.J. Hoare,
The sextet construction for cubic graphs,
Combinatorica 3, 1983, 153-165.
[Big 89] 90k:05083: N.L. Biggs, Cubic Graphs with Large Girth,
Combinatorial Mathematics: Proceedings of the Third International Conference,
Annals of the New York Academy of Sciences 555, 1989, 56-62.
[Big 93] 95h:05105: N.L. Biggs,
Algebraic Graph Theory (2nd ed.),
Cambridge University Press, 1993.
[Big 98] 99j:05097: N.L. Biggs,
Constructions for Cubic Graphs of Large Girth,
Electronic Journal of Combinatorics, 5, 1998.
[BPR 00] 2000j:05055: J. Bray, C. Parker and P. Rowley,
Cayley type graphs and cubic graphs of large girth,
Discrete Math, 214, 2000, 113-121.
[BMS 95] 96i:05138: G. Brinkmann, B. D. McKay and C. Saager,
The smallest cubic graphs of girth nine,
Combinatorics Probability and Computing 5, 1995, 1--13.
[BCN 89] 90e:05001: A.E. Brouwer, A.M Cohen and A. Neumaier.
Distance regular graphs,
Springer-Verlag, 1989.
[Exo 96]: G. Exoo.
A Simple Method for Constructing Small Cubic Graphs of Girths 14, 15 and 16.
Electronic Journal of Combinatorics, 3, 1996.
[Exo 01]: G. Exoo.
A Trivalent Graph of Girth 17,
Australasian Journal of Combinatorics, To appear 2001.
[Exo 01b]: G. Exoo.
Small Rgular Graphs of Girth Five Ars Combinatoria, To appear.
[FeH 64] 30:1189: W. Feit and G. Higman.
The non-existence of certain generalized polygons.
Journal of Algebra 1, 1964, 114 - 131.
[Hoa 93] 94j:05058: M. Hoare.
Triplets and Hexagons,
Graphs and Combinatorics 9, 1993, 225 - 233.
[HoS 93] 94j:05037: D.A. Holton and J. Sheehan,
The Petersen graph,
Australian Mathematical Society Lecture Notes 7,
Cambridge University Press, 1993.
[Mur 79] 80m:05067: U.S.R Murty,
A generalization of the Hoffman-Singleton graph,
Ars Combinatoria, 7, 1979, 191-193
[OKW 80] 81h:05085: M. O'Keefe and P.K. Wong.
A smallest graph of girth 10 and valency 3.
Journal of Combinatorial Theory (B) 29, 1980, 91 - 105.
[OKW 84] 86g:05058: M. O'Keefe and P.K. Wong.
On certain regular graphs of girth 5, Internat. J. Math. Math. Sci. 7, 1984, 785-791.
[Won 82] 83c:05080: P.K. Wong.
Cages - a survey,
Journal of Graph Theory 6, 1982, 1-22.
[Won 86] 87j:05100: P.K. Wong.
A regular graph of girth 6 and valency 11
Internat. J. Math. Math. Sci 9, 1986, 561-565.