A novel class of counting polynomials, called Cluj polynomials is proposed on the ground of Cluj matrices. The polynomial coefficients are calculated from the above matrices or by means of orthogonal edge-cuts, in case of distance-based edge-calculated version. Basic definitions and properties of the Cluj matrices and corresponding polynomials are given. Relation with other counting polynomials is evidenced. Utility of Cluj descriptors in predicting the resonance energy of a set of planar polyhexes is exemplified.
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