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Network Biology, 2025, 15(3): 67-74
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Article

Analysis of Z64 genetic code network

Adil Akhtar1, Nasrin Irshad Hussain2
1Department of Mathematics, Golaghat Engineering College, Golaghat, Assam-785621, India
2Department of Computer Application, Sibsagar University, Assam-785665, India

Received 27 November 2024;Accepted 31 December 2024;Published online 15 January 2025;Published 1 September 2025
IAEES

Abstract
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 ∈R, the vertices x and y are adjacent if x+y∈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.

Keywords amino acid;genetic code;signed graph;total graph.


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