  The graph coloring problem (GCP) is one of the most studied NP-HARD problems
in computer science. Given a graph , the task is to assign a color to all
vertices such that no vertices sharing an edge receive the same color and that
the number of used colors, is minimal. Different heuristic, meta-heuristic,
machine learning and hybrid solution methods have been applied to obtain the
solution. To solve this problem we use mutation of evolutionary algorithm. For
this purpose we introduce binary encoding for Graph Coloring Problem. This
binary encoding help us for mutation, evaluate, immune system and merge color
easily and also reduce coloring dynamically. In the traditional evolutionary
algorithm (EA) for graph coloring, k-coloring approach is used and the EA is
run repeatedly until the lowest possible is reached. In our paper, we start
with the theoretical upper bound of chromatic number, that is, maximum
out-degree + 1 and in the process of evolution some of the colors are made
unused to dynamically reduce the number of color in every generation. We test
few standard DIMACS benchmark and compare resent paper. Maximum results are
same as expected chromatic color and few data sets are larger than expected
chromatic number
