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A signed graph $\Sigma=(G,\sigma)$ is said to be parity signed if thereexists a bijection $f : V(G) \rightarrow \{1,2,...,|V(G)|\}$ such that$\sigma(uv)=+$ if and only if $f(u)$ and $f(v)$ are of same parity, where $uv$is an edge of $G$. The rna number of a graph $G$, denoted $\sigma^{-}(G)$, isthe minimum number of negative edges among all possible parity signed graphsover $G$. The rna number is also equal to the minimum cut size that has nearlyequal sides.  In this paper, for generalized Petersen graph $P(n,k)$, we prove that $3 \leq\sigma^{-}(P(n,k)) \leq n$ and these bounds are sharp. The exact value of$\sigma^{-}(P(n,k))$ is determined for $k=1,2$. Some famous generalizedPetersen graphs namely, Petersen graph $P(5,2)$, Durer graph $P(6,2)$,Mobius-Kantor graph $P(8,3)$, Dodecahedron $P(10,2)$, Desargues graph $P(10,3)$and Nauru graph $P(12,5)$ are also treated.  We show that the minimum order of a $(4n-1)$-regular graph having rna numberone is bounded above by $12n-2$. The sharpness of this upper bound is alsoshown for $n=1$. We also show that the minimum order of a $(4n+1)$-regulargraph having rna number one is $8n+6$. Finally, for any simple connected graphof order $n$, we propose an $O(2^n + n^{\lfloor \frac{n}{2} \rfloor})$ timealgorithm for computing its rna number.

RNA Number of Some Parity Signed Generalized Petersen Graphs