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Some introductory results stemming from application to degree sequences of simple connected graphs are provided in this paper. Amongst others, the result namely, that a derivative degree sequence, $d_d(G) \\in \\Bbb D_d(G)= \\{(\\lceil\\frac{d(v_1}{\\ell}\\rceil, \\lceil\\frac{d(v_2)}{\\ell}\\rceil, \\lceil\\frac{d(v_3)}{\\ell}\\rceil, ..., \\lceil\\frac{d(v_n)}{\\ell}\\rceil| \\ell = d(v_i), \\forall i,$ with $d(v_i)\\geq 2\\},$ of a simple connected graph $G$ is a parking function, is presented. 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