existence and fundamental properties of dominating induced matchings

A dominating induced matching is a subset of edges in a graph such that every edge is either in this subset or shares exactly one endpoint with an edge of it. the concept lies at the intersection of domination and matching theory. this paper introduces the fundamental notions related to dominating induced matchings, explores their existence in several graph classes. also, we investigate the relation between the size and order of a graph with dominating induced matching number.