Geodesic
Smallest Regular Graphs of Given Degree and Diameter
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 187-191

Voir la notice de l'article provenant de la source Library of Science

In this note we present a sharp lower bound on the number of vertices in a regular graph of given degree and diameter.
Keywords: regular graph, degree/diameter problem, extremal graph 
Knor, Martin. Smallest Regular Graphs of Given Degree and Diameter. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 187-191. http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a14/
@article{DMGT_2014_34_1_a14,
     author = {Knor, Martin},
     title = {Smallest {Regular} {Graphs} of {Given} {Degree} and {Diameter}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {187--191},
     year = {2014},
     volume = {34},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a14/}
}
TY  - JOUR
AU  - Knor, Martin
TI  - Smallest Regular Graphs of Given Degree and Diameter
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2014
SP  - 187
EP  - 191
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a14/
LA  - en
ID  - DMGT_2014_34_1_a14
ER  - 
%0 Journal Article
%A Knor, Martin
%T Smallest Regular Graphs of Given Degree and Diameter
%J Discussiones Mathematicae. Graph Theory
%D 2014
%P 187-191
%V 34
%N 1
%U http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a14/
%G en
%F DMGT_2014_34_1_a14

[1] E. Bannai and T. Ito, On finite Moore graphs, J. Fac. Sci. Tokyo Univ. 20 (1973) 191-208.

[2] E. Bannai and T. Ito, Regular graphs with excess one, Discrete Math. 37 (1981) 147-158. doi:10.1016/0012-365X(81)90215-6

[3] R.M. Damerell, On Moore graphs, Proc. Cambridge Philos. Soc. 74 (1973) 227-236. doi:10.1017/S0305004100048015

[4] P. Erdös, S. Fajtlowicz and A.J. Hoffman, Maximum degree in graphs of diameter 2, Networks 10 (1980) 87-90. doi:10.1002/net.3230100109

[5] A.J. Hoffman and R.R. Singleton, On Moore graphs with diameter 2 and 3, IBM J. Res. Develop. 4 (1960) 497-504. doi:10.1147/rd.45.0497

[6] M. Knor and J. Širáň, Smallest vertex-transitive graphs of given degree and diameter, J. Graph Theory, (to appear).

[7] M. Miller and J. Širáň, Moore graphs and beyond: A survey of the degree-diameter problem, Electron. J. Combin., Dynamic survey No. D14 (2005), 61pp.