On total matching numbers and total covering numbers of complementary graphs

Let G be a graph with edge set E and vertex set V. A vertex u is said to cover itself, all edges incident with u and all vertices joined to u . An edge (u, v) covers itself, the vertices u and v and all edges incident with u or v . Two elements of E U V are independent if neither covers the other . A Subset ~', of elements of E U V is called a total cover if the elements of W cover G and W is minimal ; a subset J of elements of E U V is called a total matching if the elements of J are pairwise independent and T is maximal. We shall be interested in the quantities