A Lyness equation for graphs
| dc.contributor.author | Northshield, Sam | |
| dc.date.accessioned | 2018-04-05T19:43:34Z | |
| dc.date.accessioned | 2020-06-22T14:35:29Z | |
| dc.date.available | 2018-04-05T19:43:34Z | |
| dc.date.available | 2020-06-22T14:35:29Z | |
| dc.date.issued | 2012 | |
| dc.identifier.citation | Northshield, S. (2012). A Lyness equation for graphs. Journal of Difference Equations and Applications, 18(7), 1183-1191. http://doi.org/10.1080/10236198.2011.556629 | en_US |
| dc.identifier.uri | http://hdl.handle.net/20.500.12648/1114 | |
| dc.description | This article has been published in 2011 in the Journal of Difference Equations and Applications. | en_US |
| dc.description.abstract | The 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.language | en_US | en_US |
| dc.publisher | Journal of Difference Equations and Applications | en_US |
| dc.subject | difference equation | en_US |
| dc.subject | graph | en_US |
| dc.subject | invariant | en_US |
| dc.subject | periodicity | en_US |
| dc.title | A Lyness equation for graphs | en_US |
| dc.type | Article | en_US |
| refterms.dateFOA | 2020-06-22T14:35:30Z | |
| dc.description.institution | SUNY Plattsburgh |
