Some properties of n-cut splicing on labelled semigraphs

Abstract

A semigraph is one of the generalization of graphs. Different from the hypergraph, a semigraph generalizes a graph in a straightforward manner where the edges of the graph are depicted as usual lines as in a graph, instead of sets as in a hypergraph. The vertices of the semigraph can be labelled by assigning symbols to them and the semigraph is called a labelled semigraph. In graph theory, various concepts can be applied on graphs, for instance the splicing system. Splicing system comprises of the field of formal language theory as well as discrete mathematics which focuses on the recombinants behavior of DNA molecules. Labelled semigraph can depict a problem where the labels hold certain values or properties. In DNA computing, a DNA molecule can be illustrated as a labelled semigraph where each vertex is assigned one label representing the nucleotide or base of the DNA molecule; and its cleavage pattern is described as a notion called n-cut splicing. In this research, the idea of n-cut splicing is applied on labelled semigraphs with one symbol. The number of the vertices in a component of n-cut spliced semigraph is firstly determined. Then, the form and order of the new labelled semigraphs generated by the recombination of the labelled n-cut spliced semigraphs are obtained. Besides that, this research also shows that the 180-degree structure of the newly obtained labelled semigraphs is also one of the results of the recombination.