Searching paths in directed graphs

Abstract

We describe how certain combinatorial structures can be represented as paths or cycles in a directed graph. As an example consider Gray codes of n-bit binary words: we are looking for sequences of all 2n binary words such that only one bit changes between two successive words. A convenient representation of the search space is that of a graph. The nodes are the binary words and an edge is drawn between two nodes if the node's values differ by exactly one bit. Every path that visits all nodes of that graph corresponds to a Gray code. If the path is a cycle, a Gray cycle was found.