λ-Optimality of Bipartite Digraphs

Since the underlying topology of interconnection networks are often modeled as graphs or digraphs, the connectivity and the edge(arc)-connectivity of a digraph are used to measure the reliability of networks. Restricted arc-connectivity is a more refined network reliability index than arc-connectivity. In 2007, Lutz Volkmann [L. Volkmann, Restricted arc-connectivity of digraphs, Inform. Process. Lett. 103 (2007) 234-239] introduced the concept of restricted arc-connectivity to digraphs. In 2008, Shiying Wang and Shangwei Lin [S.Y. Wang, S.W. Lin, @l^'-Optimal digraphs, Inform. Process. Lett. 108 (2007) 386-389] introduced the concept of minimum arc-degree and @l^'-optimality of digraphs. We call a strongly connected digraph a @l^'-optimal digraph if its restricted arc-connectivity is equal to its minimum arc-degree. In this paper, we study the restricted arc-connectivity of bipartite digraphs and give some sufficient conditions for a bipartite digraph to be @l^'-optimal.