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Graph coloring is one of the research areas that shaped the graph theory as we know it today. An equitable coloring of a graph G is a proper coloring of the vertices of G such that color classes differ in size by at most one. The subdivision graph S(G) of a graph G is the graph obtained by inserting a new vertex into every edge ofG. LetG1 andG2 be two graphs with vertex sets V (G1) and V (G2), respectively. The subdivision-vertex join of two vertex disjoint graphs G1 and G2 is the graph obtained from S(G1) and G2 by joining each vertex of V (G1) with every vertex of V (G2). In this paper, we find the equitable chromatic number of subdivision vertex join of cycle graph with path graph.

Equitable coloring on subdivision vertex join of cycle C_m with path P_n