Analysis of Equitable Coloring of m′- Splitting Graphs of Some Graphs

The objective of this research is to compute the equitable chromatic number for the m′- Splitting graph derived from various graph structures: path graph, cycle graph, star graph, book graph, bistar graph and ladder graph. A graph G is considered equitably k−colorable [5] if its vertex set can be partitioned into k independent color classes V1, V2, ..., Vk, meeting the condition ||Vi| − |Vj|| ≤ 1 for all different pairs of (i, j). The smallest integer k fulfilling this criterion is known as the equitable chromatic number of the graph G [6].