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Let $P(G,lambda)$ be a chromatic polynomial of a graph $G.$ Two graphs $G$ and $H$ aresaid to be chromatically equivalent, denoted $Gsim H,$ if $P(G,l)=P(H,l).$We write $[G]={H,|,Hsim G}.$ 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 numberof 5-independent 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 chromaticallyunique complete 4-partite graphs with certain star or matching deleted

Chromaticity of complete 4-partite graphs with certain star or matching deleted