The representation of n-cutting site splicing languages for a single string with palindromic rule via de Bruijn graph

Yusof-Goode (Y-G) splicing system proposed by Yusof illustrates the deoxyribonucleic acid (DNA) splicing
process in a luminous way, where the rule is written in a double triple notation. In the process of generating splicing
languages, DNA molecules are cut and pasted, based on the reaction of the molecules with restriction enzyme and ligase.
The resulting molecules, either in original or new molecules can be classified mathematically in the form of limit, adult or
transient languages. Conducting a wet lab experiment to produce splicing languages is a huge investment, thus
mathematical approach is one of the best options in predicting the outcome on splicing languages when n-cutting site exist
in a splicing process. Besides the generation of splicing languages through splicing system, a meaningful representation of
the languages can be portrayed in a graph. In this paper, the n-cutting site splicing languages generated from Y-G splicing
system containing single string with 2-cutting site, with palindromic rule and palindromic crossing site is investigated. The
features of left and right contexts of the rule are considered in the two cases discussed in this paper. Besides, two new
definitions namely connectors and sub-connectors are given and are adopted in the generation of de Bruijn graph. With the
constructed de Bruijn graph for the resulting splicing languages from both cases, a theorem is proposed.