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

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

Offset

3,7

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

Links

Table of n, a(n) for n=3..12.

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)

Example

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.

Crossrefs

Cf. A000066 (size of these graphs).

Sequence in context: A040322 A040323 A321260 * A040315 A040316 A135216

Adjacent sequences: A052450 A052451 A052452 * A052454 A052455 A052456

Keyword

nonn,more,hard

Author

Eric W. Weisstein

Extensions

a(11) from Brendan McKay and W. Myrvold

Status

approved