A064513 Maximal number of nodes in graph of degree <= n and diameter 2 (another version).

2, 5, 10, 15, 24, 32, 50

Offset

1,1

Comments

Comment from Allan C. Wechsler, Nov 22 2015: a(8) <= 65 by the Moore bound. Since 8 is not in {2,3,7,57}, we know a(8) <= 64. I don't know if we have any better upper bounds. This seems like a decent undergraduate research project. Pushing up the lower bound also.

Links

Table of n, a(n) for n=1..7.

F. Comellas, (Degree,Diameter) Problem for Graphs

J. Dinneen, Michael; Hafner, Paul R., New Results for the Degree/Diameter Problem, Networks 24 (1995), 359-367, arXiv:math/9504214 [math.CO], 1995.

Alan J. Hoffman, Robert R. Singleton, Moore graphs with diameter 2 and 3, IBM Journal of Research and Development 5 (1960), 497-504.

Eyal Loz, Jozef Siran, New record graphs in the degree-diameter problem, Australasian Journal of Combinatorics 41 (1968), 63-80.

Brendan McKaya, Mirka Miller, Jozef Širáň, A note on large graphs of diameter two and given maximum degree, Journal of Combinatorial Theory Series B 74 (1968): 110-118.

Mirka Miller, Jozef Sirán, Moore Graphs and Beyond: A survey of the Degree/Diameter Problem, Electronic Journal of Combinatorics, Dynamic Survey DS14.

Guillermo Pineda-Villavicencio; José Gómez; Mirka Miller, Hebert Pérez-Rosés, New Largest Graphs of Diameter 6, Electronic Notes in Discrete Mathematics 24 (2006), 153-160.

Wikipedia, Table of the largest known graphs of a given diameter and maximal degree

Wikipedia, Hoffman-Singleton Graph

Example

a(2) = 5 is achieved by the 5-cycle.
a(3) = 10 is achieved by the Petersen graph.

Crossrefs

Sequence in context: A013927 A163059 A099738 * A117582 A002134 A243971

Adjacent sequences: A064510 A064511 A064512 * A064514 A064515 A064516

Keyword

nonn,nice,hard,more

Author

N. J. A. Sloane, Oct 07 2001

Extensions

It is known that a(8) >= 57.

Corrected and extended by N. J. A. Sloane, Nov 17 2015 following suggestions from Allan C. Wechsler and Christopher E. Thompson.

Status

approved