

A361517


The value of n for which the twoplayer impartial {0,1}Toggle game on a generalized Petersen graph GP(n,2) with a (1,0)weight assignment is a nextplayer winning game.


3



3, 4, 5, 11, 17, 27, 35, 37, 49, 59, 69, 81, 91, 103, 115, 123, 135, 137, 167, 175, 189, 199, 207, 287, 295, 307, 361, 1051, 2507, 2757, 2917, 3057, 3081, 7255, 7361, 7871, 16173
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OFFSET

3,1


COMMENTS

The twoplayer impartial {0,1}Toggle game is played on a simple connected graph G where each vertex is assigned an initial weight of 0 or 1.
A Toggle move consists of selecting a vertex v and switching its weight as well as the weights of each of its neighbors. This move is only legal provided the weight of vertex v is 1 and the total sum of the vertex weights decreases.
In the special case G=GP(n,2), a (1,0)weight assignment is one in which each vertex of the outer polygon is assigned weight 1 and each vertex of the inner polygon(s) is assigned weight 0.


REFERENCES

E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001.


LINKS



EXAMPLE

For n = 3, the {0,1}Toggle game on GP(3,2) with a (1,0)weight assignment is a nextplayer winning game.
For n = 5, the {0,1}Toggle game on GP(5,2) with a (1,0)weight assignment is a nextplayer winning game.


PROG

(CGSuite) # See Levandosky link


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



