Weighted Hosoya polynomials have been developed by Diudea, in ref. Studia Univ. "Babes-Bolyai", 2002, 47, 131-139. Among various weighting schemes, those polynomials obtained by using Diudea's Shell matrix operator are far more interesting. We present here the Shell-Distance and Shell-Degree-Distance polynomials and close formulas to calculate them and derived Cluj-Tehran CT index in the family of square tiled tori T(4,4)S[5,n]. Applications of the proposed descriptors are also presented.
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