The queen graph coloring problem consists in covering a n x n chess board with n^2 queens in such a manner that two queens of the same color cannot attack each other. When the size, $n$, of the chess board is not a multiple of 2 or 3 it is difficult to color the queen graph with only n colors. We have developed an exact algorithm which is able to solve exhaustively this problem for dimension up to n=12 and finds a solution for n=14 in one week computing time. The 454 solutions of queen-12 show horizontal and vertical symmetries. Starting from this observation we design a new exact, but incomplete, algorithm which leads us to color queen-n problems with n colors for n=15,16,18,20,21,24 and 28 in less than one day computing time. In this paper we recall briefly the main characteristics of the first search tree algorithm then we describe the four kinds of geometric operations we have used to improve significantly our results.