Questions on Orbital Graphs
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Previous work on orbital graphs has shown that they are a powerful pruning tool in backtrack algorithms. In this article we consider a few questions that are relevant from this perspective, focussing on properties of orbital graphs that can be detected by an efficient algorithm. Roughly speaking, the challenge is to decide when to use orbital graphs and, possibly, how to choose a “best” orbital graph, and to make this decision early in the algorithm at low computational costs. In this note we discuss how to decide whether or not a given digraph is an orbital graph for some group and what groups are recognisable by their orbital graphs (or even just one orbital graph). We approach these problems from a theoretical point of view.
KeywordsOrbital graphs Backtrack search Permutation groups
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