Inthis study some algebraic connections in genetic code is being discussed.The genetic code is the rule by which DNA stores the geneticinformation about formation of protein molecule. Based on the physico-chemicalproperties of four RNA (or DNA) bases, two orders in the base sets are obtained. This ordering allows us to define a ringstructure on the set of 64 codons. Then the total graph in the genetic codealgebra is being discussed. It is shown that transition mutations (purine (A,G) to purine or pyrimidine (C, T) to pyrimidine) on the third base position ofcodons partitions the whole set of codons into disjoint graphs and therebygenerates the total graph of the genetic code. The redundancy of the 64 codonscoding for the 20 amino acids is reduced by the total graph.
