Abstract
We study the properties of a knot K to be 2-adjacent to another knot W by analyzing their Conway polynomials, Jones polynomials and Homfly polynomials and give some very useful conditions. We discuss whether each pair of knots can be 2-adjacent to each other, i.e. whether 2-adjacency is a symmetric relation. We discuss also whether the trivial knot, the trefoil knot and the figure-eight knot can be 2-adjacent to any knot in Rolfsen's table and the opposite cases, except for 934 it is not decided whether it is 2-adjacent to 41. Finally, we give some examples to answer I. Torisu's problem partly and etc.
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