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The critical group from a cryptographic perspective
Author(s) -
Biggs Norman
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm070
Subject(s) - mathematics , cryptography , abelian group , construct (python library) , theoretical computer science , perspective (graphical) , group (periodic table) , graph , cryptographic primitive , discrete mathematics , combinatorics , cryptographic protocol , computer science , algorithm , computer network , chemistry , geometry , organic chemistry
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 with critical groups that are cyclic, and discuss the associated computational problems using algorithms based on the theory of ‘chip‐firing’.