This site is supported by donations to The OEIS Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A064513 Maximal number of nodes in graph of degree <= n and diameter 2 (another version). 1


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

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

%C 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.

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

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

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

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

%H F. Comellas, <a href="http://maite71.upc.es/grup_de_grafs/grafs/taula_delta_d.html">(Degree,Diameter) Problem for Graphs</a>

%H J. Dinneen, Michael; Hafner, Paul R., <a href="http://arxiv.org/abs/math/9504214">New Results for the Degree/Diameter Problem</a>, Networks 24 (1995), 359-367, arXiv:math/9504214.

%H Mirka Miller, Jozef Sirán, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/DS14">Moore Graphs and Beyond: A survey of the Degree/Diameter Problem</a>, Electronic Journal of Combinatorics, Dynamic Survey DS14.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Table_of_the_largest_known_graphs_of_a_given_diameter_and_maximal_degree">Table of the largest known graphs of a given diameter and maximal degree</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hoffman%E2%80%93Singleton_graph">Hoffman-Singleton Graph</a>

%e a(2) = 5 is achieved by the 5-cycle.

%e a(3) = 10 is achieved by the Petersen graph.

%K nonn,nice,hard,more

%O 1,1

%A _N. J. A. Sloane_, Oct 07 2001

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

%E Corrected and extended by _N. J. A. Sloane_, Nov 17 2015 following suggestions from _Allan C. Wechsler_ and _Christopher E. Thompson_.

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 22 12:10 EDT 2019. Contains 326177 sequences. (Running on oeis4.)