Abstract
Lomonaco and Kauffman introduced knot mosaics in their work on quantum knots. This definition is intended to represent an actual physical quantum system. A knot n-mosaic is an n×n matrix of 11 kinds of specific mosaic tiles representing a knot or a link. In this paper, we consider the alternating mosaic number of an alternating knot K which is defined as the smallest integer n for which K is representable as a reduced alternating knot n-mosaic. We define a signed mosaic graph and a diagonal grid graph and construct Hamiltonian cycles derived from the diagonal grid graphs. Using the cycles, we completely determine the alternating mosaic number of torus knots of type (2,q) for q≥2, which grows in an order of q1/2.
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