In this paper, we propose a novel non-hybrid discrete firefly algorithm (DFA) for solving planar graph coloring problems. The original FA handles continuous optimization problems only. To apply it to discrete problems, we should redefined the original FA over discrete space. In this work, we introduce a new algorithm based on Similarity and discretize FA directly without any other hybrid algorithm. The experiments show that the proposed method outperforms the success rate of HDPSO and HDABC when solving planar graph coloring problems.