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Some 2-D and 3-D graphical representation of DNA sequences have been given by Nandy, Leong and Mogenthaler, and Randic et al., which give visual characterizations of DNA sequences, and a number of different approaches have been developed to date on numerically characterizing DNA sequences, but application of such method to practical problems still remains a formidable task. In this paper, we presented a novel graphical representation of DNA sequences by taking four special vectors in 2D Cartesian coordinate system to represent the four nucleic acid bases in DNA sequences, so that a DNA sequence is denoted on a plane by a directed walk. The comparison between sequences thus becomes one between the corresponding graphs. With a so-generated graphical representation of DNA, some numerical descriptors to discriminate gene sequences on the basis of distribution patterns are considered. The designed program can plot quickly not only the graphical representation of DNA sequence, but also calculate out the values of the normalized mean moments and other numerical parameters. The preliminary results in this paper show that the novel 2D graphical representation and the selected set of DNA numerical descriptors are able to discriminate between conserved mammalian gene sequences.