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A Self-Stabilizing Distributed Algorithm to Construct BFS Spanning Trees of a Symmetric Graph

We propose a simple and efficient self-stabilizing distributed algorithm to construct the breadth first search (BFS) spanning tree of an arbitrary connected symmetric graph. We develop a completely new direct approach of graph theoretical reasoning to prove the correctness of our algorithm. The approach seems to have potential to have applications in proving correctness of other self-stabilizing algorithms for graph theoretical problems.