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In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and theproduct of the chromatic number of a graph and its complement, in terms of theorder of the graph. Since then, any bound on the sum and/or the product of aninvariant in a graph $G$ and the same invariant in the complement $G^c$ of $G$is called a Nordhaus-Gaddum type inequality or relation. The Nordhaus-Gaddumtype inequalities for connectivity have been studied by several authors. For abipartite graph $G=G[X,Y]$ with bipartition ($X,Y$), its bipartitecomplementary graph $G^{bc}$ is a bipartite graph with $V(G^{bc})=V(G)$ and$E(G^{bc})=\{xy:\ x\in X,\ y\in Y$ and $xy \notin E(G)\}$. In this paper, weobtain the Nordhaus-Gaddum type inequalities for connectivity of bipartitegraphs and its bipartite complementary graphs. Furthermore, we prove that theseinequalities are best possible.

The connectivity of a bipartite graph and its bipartite complementary graph