

A054760


Table T(n,k) = order of (n,k)cage (smallest nregular graph of girth k), n >= 2, k >= 3, read by antidiagonals.


22



3, 4, 4, 5, 6, 5, 6, 8, 10, 6, 7, 10, 19, 14, 7, 8, 12, 30, 26, 24, 8, 9, 14, 40, 42, 67, 30, 9, 10, 16, 50, 62
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OFFSET

0,1


REFERENCES

P. R. Christopher, Degree monotonicity of cages, Graph Theory Notes of New York, 38 (2000), 2932.


LINKS

Andries E. Brouwer, Cages


FORMULA

T(k,g) >= A198300(k,g) with equality if and only if: k = 2 and g >= 3; g = 3 and k >= 2; g = 4 and k >= 2; g = 5 and k = 2, 3, 7 or possibly 57; or g = 6, 8, or 12, and there exists a symmetric generalized g/2gon of order k  1.  Jason Kimberley, Jan 01 2013


EXAMPLE

First eight antidiagonals are:
3 4 5 6 7 8 9 10
4 6 10 14 24 30 58
5 8 19 26 67 80
6 10 30 42 ?
7 12 40 62
8 14 50
9 16
10


CROSSREFS

Orders of cages: this sequence (n,k), A000066 (3,n), A037233 (4,n), A218553 (5,n), A218554 (6,n), A218555 (7,n), A191595 (n,5).


KEYWORD



AUTHOR



EXTENSIONS

Edited by Jason Kimberley, Apr 25 2010, Oct 26 2011, Dec 21 2012, Jan 01 2013


STATUS

approved



