Deoxyribonucleic Acid(DNA)contains the genetic code, which includes comprehensive infor- mation for protein synthesis in every human cell. Each gene encodes for the same protein, but the majority of DNA sequences are not coded. In addition to this non-coding portion of DNA, there is another repetition in the form of DNA triplets (codons) that match a specific amino acid code. A codon is a triplet of nucleotides that specifies each amino acid. Nucleotides are classified into four types: adenine(A), guanine(G), cytosine(C), and thymine(T). From a bio- logical standpoint, the genetic code has 64 potential alterations or combinations of three-letter nucleotide groups that may be generated using the four nucleotides. The goal of this project is extending the canonical genetic code by add two more bases to the original four by studying the genetic code’s structure using graph theory.