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dc.contributor.authorNorthshield, Sam
dc.date.accessioned2018-04-05T19:43:34Z
dc.date.available2018-04-05T19:43:34Z
dc.date.issued2012
dc.identifier.citationNorthshield, S. (2012). A Lyness equation for graphs. Journal of Difference Equations and Applications, 18(7), 1183-1191. http://doi.org/10.1080/10236198.2011.556629en_US
dc.identifier.urihttp://hdl.handle.net/1951/69914
dc.descriptionThis article has been published in 2011 in the Journal of Difference Equations and Applications.en_US
dc.description.abstractThe Lyness equation, x(n+1)=(x(n)+k)/x(n-1), can be though of as an equation defined on the 2-regular tree T2: we can think of every vertex of T2 as a variable so that if x and z are the vertices adjacent to y, then x,y,z satisfy xz=y+k. This makes sense for any 2-regular graph. We generalize this to 3-regular graphs by considering xyz=w+k and xy+xz+yz=w+k where x,y,z are the three neighbors of w. In the special case where an auxiliary condition x+y+z=f(w) also hold, a solutions is determined by (any) two values and, in some cases, an invariant can be found.en_US
dc.languageen_USen_US
dc.publisherJournal of Difference Equations and Applicationsen_US
dc.subjectdifference equationen_US
dc.subjectgraphen_US
dc.subjectinvarianten_US
dc.subjectperiodicityen_US
dc.titleA Lyness equation for graphsen_US
dc.typeArticleen_US


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