Investigating Evolutionary Relationships between Species through the Light of Graph Theory Based on the Multiplet Structure of the Genetic Code

Investigating evolutionary relationship between various species through similarity/dissimilarity analysis is a fundamental method. In this present work firstly 20 canonical amino acids and 3 stop codons (terminations) are classified into five different classes depending upon their frequency mapping with 64 codons of genetic table. Secondly, each DNA sequence is represented by a weighted directed multi graph based on that classification. Thirdly, the procedure has been implemented to find out the evolutionary relationship between various species of alpha globin and beta globin genes. Here a new mathematical tool has been constructed to derive similarity/dissimilarity matrix, to get suitable phylogenetic trees for each data set. It is completely alignment free approach and hence the time complexity is directly proportional to the sequence length, that is O(N). Moreover the classification rule will decrease the complexity of graph constructions.