The goal of this article is to examine the ideas of co-neutrosophic multi-dominating (CNMD) set, number πΎ πΆπππ· in a co-neutrosophic graph (πΊ πΆπ ) and their inversesrespectively. For specific classes of co-neutrosophic graphs (πΊ πΆπ ), the πΎ πΆπππ· and πΎ πΆπππ· β1 calculated and constraints on the corresponding πΎ πΆπππ· drived. Also, some example for evaluation the inverse co-neutrosophic domination provided.