On the relations of graph parameters and its total parameters

In this paper we get some relations between α(G), α′(G), β(G), β′(G) and α T (G), β T (G). And all bounds in these relations are best possible, where α(G), α′(G), β(G), β′(G), α T (G) and β T (G) are the covering number, edge-covering number, independent number, edge-independent number (or matching number), total covering number and total independent number, respectively.