On perfect colorings of the distance-2 graph of the 24-cube
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چکیده
A vertex 2-coloring of a graph is said to be perfect with parameters (aij) k i,j=1 if for every i, j ∈ {1, ..., k} every vertex of color i is adjacent with exactly i vertices of color j. We consider the perfect 2-colorings of the distance-2 graph of the 24-cube {0, 1}24 with parameters ((20+ c, 256− c)(c, 276− c)) (i.e., with eigenvalue 20). We prove that such colorings exist if c = 3, 6, 8, 9, 11, 12, 14, 15, 16, ..., 128 and do not exist if c = 1, 2, 4, 5.
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A vertex coloring of a graph is said to be perfect with parameters (aij) k i,j=1 if for every i, j ∈ {1, ..., k} every vertex of color i is adjacent with exactly aij vertices of color j. We consider the perfect 2-colorings of the distance-2 graph of the 24-cube {0, 1}24 with parameters ((20+ c, 256− c)(c, 276− c)) (i.e., with eigenvalue 20). We prove that such colorings exist for all c from 1 t...
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تاریخ انتشار 2009