A006856 Maximal number of edges in n-node graph of girth at least 5.

0, 1, 2, 3, 5, 6, 8, 10, 12, 15, 16, 18, 21, 23, 26, 28, 31, 34, 38, 41, 44, 47, 50, 54, 57, 61, 65, 68, 72, 76, 80, 85, 87, 90, 95, 99, 104, 109, 114, 120, 124, 129, 134, 139, 145, 150, 156, 162, 168, 175, 176, 178, 181

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

From Brendan McKay, Mar 09 2022: (Start)

The unique graph for a(50)=175 is the Hoffman-Singleton graph.

a(53) is at least 181. (End)

a(53) is exactly 181. a(54)-a(56) are at least 185,189,193. - Brendan McKay, Jan 07 2023

References

• Brendan McKay, personal communication.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• J. Backelin, Sizes of the extremal girth 5 graphs of orders from 40 to 49, arXiv preprint arXiv:1511.08128 [math.CO], 2015.
• Michael Codish, Alice Miller, Patrick Prosser, and Peter J. Stuckey, Breaking Symmetries in Graph Representation, IJCAI 2013.
• David K. Garnick, Y. H. Harris Kwong and Felix Lazebnik, Extremal Graphs without Three-Cycles or Four-Cycles, Journal of Graph Theory, 17 (1993), 633-645.
• Brendan McKay, Extremal Graphs and Turan Numbers.
• Alice Miller and Michael Codish, Graphs with girth at least 5 with orders between 20 and 32, arXiv:1708.06576 [math.CO], 2017.

Crossrefs

Cf. A159847.

Extensions

Two more terms from David Garnick (dgarnick(AT)gmail.com), Jan 09 2007

Two more terms from Michael Codish, Apr 07 2013

Definition clarified by Jörgen Backelin, Jun 18 2015

a(33)-a(52) from Brendan McKay, Mar 09 2022

a(53) from Brendan McKay, Jan 06 2023