Finding the Pancyclicity and Vertex connectivity for a general graph is the problem in NP complete class. In this paper, a bio-computation way of solving these two problems has been proposed. DNA computation is more powerful because of its massive parallelism and high density storage capacity. Thereby, producing the VERTEXCONNECTIVITY, PANCYCLIC and GIRTH algorithm solvable in polynomial time. The method in tracing the k-cycle and k-cut vertex was also used for the computation.