Non-degenerate graphical representation of DNA sequences and its applications to phylogenetic analysis.

In this paper, we propose a new 3-D graphical representation of a DNA sequence and prove that it has two properties: (1) there is no circuit in the graph; (2) there exists a one-to-one correspondence between a DNA sequence and the graph. These properties guarantee it has nondegeneracy. Based on the 3-D graphical representation, we characterize a DNA sequence by a 12-dimensional vector whose components are normalized ALE-indexes of the corresponding L/L matrices.