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Let P k (x) denote the polynomial of the path on k vertices. A complete description of the matrix that is the obtained by evaluating P k (x) at the adjacency matrix of the complete graph, along with computing the effect of evaluating P k (x) with Laplacian matrices of a path and of a circuit.doi:10.13001/1081-3810.1103 fatcat:7xggt4kpqbcp5okhqnpivuigfq