Smallest Regular Graphs of Given Degree and Diameter

• Autorzy: Martin Knor
• Języki publikacji: EN

Abstrakty

EN

In this note we present a sharp lower bound on the number of vertices in a regular graph of given degree and diameter.

Słowa kluczowe

EN

regular graph; degree/diameter problem; extremal graph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 1
• Strony: 187-191

Daty

wydano

2014-02-01

online

2014-02-14

Twórcy

autor

Martin Knor

• Slovak University of Technology in Bratislava Faculty of Civil Engineering, Department of Mathematics Radlinsk´eho 11, 813 68 Bratislava

Bibliografia

• [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[Crossref]
• [3] R.M. Damerell, On Moore graphs, Proc. Cambridge Philos. Soc. 74 (1973) 227-236. doi:10.1017/S0305004100048015[Crossref]
• [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[Crossref]
• [6] M. Knor and J. Širáň, Smallest vertex-transitive graphs of given degree and diameter, J. Graph Theory, (to appear).[WoS]
• [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.

Identyfikatory

DOI

10.7151/dmgt.1702