A052453 Number of nonisomorphic (3,n) cage graphs.

1, 1, 1, 1, 1, 1, 18, 3, 1, 1

Offset: 3

Author

Eric W. Weisstein

Keywords

• nonn
• more
• hard

Comments

A (3,n) cage graph is a 3-regular (or cubic, or trivalent) graph which has girth n, and has the fewest possible number of vertices. - Harry Richman, Jan 14 2025

Examples

			a(3) = 1 since the complete graph K_4 is the unique smallest cubic graph with girth 3.
a(5) = 1 since the Petersen graph is the unique smallest cubic graph with girth 5.
a(12) = 1 from the unique generalized hexagon of order 2.
		

Links

• Andries E. Brouwer, Cages
• Geoffrey Exoo, Regular graphs of given degree and girth.
• Geoffrey Exoo and Robert Jajcay, Dynamic cage survey, Electr. J. Combin. (2008, 2011).
• Gordon Royle, Cages of higher valency
• Eric Weisstein's World of Mathematics, Cage Graph (claims too much)
• Wikipedia, Cage (graph theory)

Crossrefs

Cf. A000066 (size of these graphs).

Extensions

a(11) from Brendan McKay and W. Myrvold