Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2006-07

June 2006

The Critical Group from a Cryptographic Perspective

Norman Biggs

The critical group of a graph is an abelian group that arises in several contexts, and there are some similarities with the groups that are used in cryptography. We construct a family of graphs whose critical groups are cyclic, and discuss the associated computational problems using algorithms based on the theory of ‘chip-firing’.

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