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A361517
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The value of n for which the two-player impartial {0,1}-Toggle game on a generalized Petersen graph GP(n,2) with a (1,0)-weight assignment is a next-player winning game.
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3
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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
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3,1
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COMMENTS
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The two-player 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.
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REFERENCES
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E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001.
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LINKS
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EXAMPLE
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For n = 3, the {0,1}-Toggle game on GP(3,2) with a (1,0)-weight assignment is a next-player winning game.
For n = 5, the {0,1}-Toggle game on GP(5,2) with a (1,0)-weight assignment is a next-player winning game.
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PROG
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(CGSuite) # See Levandosky link
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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