1,3

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).

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

Sequence in context: A067603 A065299 A128942 this_sequence A098556 A159585 A130334

Adjacent sequences: A135442 A135443 A135444 this_sequence A135446 A135447 A135448

nonn,uned

Yasutoshi Kohmoto zbi74583(AT)boat.zero.ad.jp, Feb 18 2008