The study explores the use of a MATLAB program to prove the theorem that fan graphs admit sum 3-equitable labeling. The labeling scheme is defined as a bijective transformation, which assigns integer values to the vertices of the graph. These values are then used to determine the edge values, which are computed on the sum of the values of the vertices the edge joins modulo three. This classification primarily requires the preservation of equitability, which means the edges labeled via the transformation must almost evenly lie in the three classes, such that the absolute value of edges in any two classes differs by no more than one.