Co-odd domination in graphs

A dominating set D in a graph is a subset of its vertex set such that every vertex of either belongs to D or is adjacent to at least one vertex of D. A dominating set D in a graph with vertex set V is said to be a co-odd dominating set if the degree of every vertex belonging to V \D is odd.A co-odd dominating set is minimum if it contains the least possible vertices.The size of a minimum co-odd dominating set in a graph is called the co-odd domination number of .In this paper, we establish some fundamental properties and bounds of the co-odd domination number.We also determine the co-odd domination numbers of several well-known graphs and their complements.