A135445 Number of fixed points of N_{2,2}(G_n).

1, 1, 2, 4, 10

Offset

1,3

Comments

G_n are connected graphs of n nodes.

N_{m,n} is a mapping form k nodes graph to k nodes graph. N is for "Near" [Definition] For all pairs of distinct vertices x,y in G if n paths of length m exist between x and y then add an edge xy. The graph H which is made from G is represented as N_{m,n}(G).

Links

Table of n, a(n) for n=1..5.

Example

Example: N_{1,1}(G)=G. Other definition of N_{2,3}: G={V,E_g}, H=N_{2,3}(G), H={V,E_h}. All x,y (x,y E V and -x=y and (Exist p,q,r -p=q and -p=r and -q=r and xp,xq,xr,py,qy,ry E E_g)) - E_h = E_g U {xy} where "E" means "element" and "-" means "not"
Fixed points of N_{2,2}: n = number of nodes. We count only connected graphs.
n=1
....o
n=2
....o_o
n=3
....o_o_o....o_o
.............|/
.............o
n=4
....o_o_o_o....o_o_o....o_o_o....o_o
.................|......|/.......|x|
.................o......o........o_o
n=5
....o_o_o_o_o....o_o_o_o....o_o_o_o....o_o_o......o_o_o_o
...................|........|/.........|...|........|/...
...................o........o..........o___o........o....
.....................................................
.........o_o_o.....o_o_o.....o_o_o......o_o_o....o_o_o
........../|.......|/|.......|/.........|x|......|x-x|
.........o.o.......o.o.......o_o........o_o......o___o
..................................................K_5
.........o_o....o_o
.........|.|....|/|
.........o_o....o_o
These graphs don't have the following subgraphs:
o_o ... o_o
| | ... |/|
o_o ... o_o

Crossrefs

Sequence in context: A364637 A328837 A302349 * A098556 A159585 A130334

Adjacent sequences: A135442 A135443 A135444 * A135446 A135447 A135448

Keyword

nonn,uned

Author

Yasutoshi Kohmoto, Feb 18 2008

Status

approved