CHROMATICITY OF COMPLETE 4-PARTITE GRAPHS WITH CERTAIN STAR OR MATCHING DELETED

Let P(G, γ) be a chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G ~ H, if P(G, γ) = P(H, γ). We write [G] = {H|H ~ G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 4-partite graphs G accordingly to the number of 5-indepcndent partitions of G. Using these results, we investigate the chromaticity of G with certain star or matching deleted. As a by-product, we obtain new families of chromatically unique complete 4-partitc graphs with certain star or matching deleted.