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  1. Node-Kayles is an impartial game played on a simple graph. The Sprague-Grundy theorem states that every impartial game is associated with a nonnegative integer value called a Nimber. This paper studies the Nimber sequences of various families of graphs, including 3-paths, lattice graphs, prism graphs, chained cliques, linked cliques, linked cycles, linked diamonds, hypercubes, and generalized Petersen graphs. For most of these families, we determine an explicit formula or a recursion on their Nimber sequences.