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In traditional cancer diagnosis process, pathologists manually examine biopsies to make diagnostic assessments. The assessments are largely based on visual interpretation of cell morphology and tissue distribution, lacking of quantitative measures. Therefore, they are subject to considerable inter-observer variability. To circumvent this problem, numerous studies aim at quantifying the characteristics of cancerous cells and tissues that distinguish them from their counterparts. Such quantification facilitates to design automated systems that operate on quantitative measures, and in turn, to reduce the inter-observer variability. There is a computational model available that relies solely on the topological features of cancerous cells in a tumor. Despite their complex dynamic nature, the self-organizing clusters of cancerous cells exhibit distinctive graph properties that distinguish the cancerous tissue from non-cancerous tissues; e.g. from a healthy tissue or an inflamed tissue. It is difficult to distinguish a cancerous tissue sample visually from an inflamed one. It is possible to construct a graph of the cells (cell graph) based on the location of the cells in the low-magnification image of a tissue sample surgically removed from a human patient. Assuming the cells present in a sample as the vertices of the cell graphs and the edges connecting those vertices/cells we can construct the cell graphs. There is a possibility of implementing the technique of using cell graphs to detect cancerous sample biopsies using some simple or a little bit complex computational techniques. Here possibly a new way is going to be introduced in this field, which is an application of graph coloring using the cell graphs to classify the normal, cancerous and inflamed sample biopsies. This work intends to automate the solution to the problem of identifying cancerous sample biopsies applying customized graph Coloring method solving by Genetic Algorithm on the cell graphs.