Given an alphabet $\mathrm{\Sigma }$ and a finite minimal set $B$ of forbidden words, a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any string in $B$ as their substrings. From the fact that a string in the language is equivalent to a path in the corresponding graph, we have obtained a polynomial time algorithm by modifying the power of the adjacency matrix in the graph.