In order to read a DNA sequence

Blazewicz et al.propose the definition of(α

k)-labeled digraphs.A digraph D is called a DNA graph if D is(4

k)-labeled.Sufficient and necessary conditions for directed paths and directed cycles to be(α

k)-labeled are proved.Let T be an oriented tree with only one vertex u satisfied that the in(out)-degree of u is 0.A necessary condition for T to be(α

k)-labeled and a sufficient and necessary condition for T to be a DNA graph are also proved.