Molecular biology aims to study DNA and protein structure, that is the recognition of DNA primary structure. In order to do that, a mathematical model based on graph theory has been developed in recent years. Mainly, suitably defined digraphs are presented. A digraph built from the spectrum (a set of some k-long oligonucleotides) as follows: each oligonucleotide from the spectrum becomes a vertex, two vertices are connected by an arc if the i rightmost nucleotides of the first point overlap with the i leftmost nucleotides of the second one. We refer to these graphs as DNA graphs and DNA labelled graphs depending on whether the oligonucleotides used are distinct or not. In this thesis, we study the digraphs mentioned above and characterize DNA labelled graphs which are also DNA graphs, especially when the order (number of vertices) is small