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 A135445 Number of fixed points of N_{2,2}(G_n). 0
 1, 1, 2, 4, 10 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 28 12:54 EDT 2024. Contains 372913 sequences. (Running on oeis4.)