Adil Akhtar Nasrin Irshad Hussain Department of Mathematics, Golaghat Engineering College, Golaghat, Assam-785621, India Department of Computer Application, Sibsagar University, Assam-785665, India Network Biology ISSN 2220-8879 http://www.iaees.org/publications/journals/nb/online-version.asp 2025 15 3 67 74 International Academy of Ecology and Environmental Sciences Hong Kong 27 November 2024 31 December 2024 1 September 2025 amino acid genetic code signed graph total graph The genetic code is the set of rules defining how the sequence of nucleotides in DNA or RNA determines the specific amino acid sequence in the synthesis of protein. Proteins are the basic functional elements of living organisms and amino acids are the building blocks of proteins. Each protein is formed by a linear chain of amino acids. The DNA consists of two complementary long chains of nucleotides, viz. Adenine (A), Cytosine (C), Guanine (G) or Thymine (T) (Uracil (U) in case of RNA). Three consecutive DNA nucleotides form a codon. Each codon specifies a particular amino acid. The set of 64 codons can be equipped with a ring structure isomorphic to the ring of integers modulo 64 (Z64). Different graph structures can be generated from a ring. In this paper we have discussed total graph in this ring. Total graph of a ring R is an undirected graph where vertex set is the set of all elements of the ring and for distinct x, y belong to R, the vertices x and y are adjacent if x+y belongs to Z(R), where Z(R) be the set of zero divisor of R. In this manuscript using signed graph we have try to explain that the graph of the genetic code is an unbalanced graph. http://www.iaees.org/publications/journals/nb/articles/2025-15(3)/analysis-of-Z64-genetic-code-network.pdf