Structural analysis of invertible graphs

Reliability is an important issue in systems architecture. This paper focuses on a new class of invertible networks which are more reliable in the sense that if there is a failure in the physical components of the system then there always exists an alternate set of nodes to carry out the job in the complement. A graph G is said to be invertible if there exists an inverse vertex cover in G. The contribution of this paper is a new algorithm for recognizing invertible graphs. Our algorithm runs in linear time and is computationally very simple. We present a characterization for invertible graphs in terms of the breadth first search tree and thereby study their theoretical properties.