Generalized Graph Product and its Application on Generating Solutions of the Millennium n-Queens Problem
O. Kolossoski, Luiz Carlos Matioli, Elvis Manuel Rodriguez Torrealba, J.G. Silva · REMAT Revista Eletrônica da Matemática · 2022
The generalized Kronecker graph product was introduced by Figueroa-Centeno et al. (2008). Later, Baca et al. (2018) used it for obtaining solutions of the n-queens problem on larger boards from solutions on smaller boards. In this paper, we generalize the graph product and the recent results by Baca et al. (2018), obtaining a larger class of solutions by knowing solutions on lower size boards in advance. We finalize the paper stating a couple of conjectures regarding conditions for obtaining composite solutions via graph product.