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In graph theory, the shift graph Gn,k for n , k ∈ N , n > 2 k > 0 {\displaystyle n,k\in \mathbb {N} ,\ n>2k>0} is the graph whose vertices correspond to the ordered k {\displaystyle k} -tuples a = {\displaystyle a=} with 1 ≤ a 1 < a 2 < ⋯ < a k ≤ n {\displaystyle 1\leq a_{1}
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