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    A Lyness equation for graphs

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    Date
    2012
    Author
    Northshield, Sam
    Publisher
    Journal of Difference Equations and Applications
    Metadata
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    Subject
    difference equation
    graph
    invariant
    periodicity
    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.
    Description
    This article has been published in 2011 in the Journal of Difference Equations and Applications.
    URI
    http://hdl.handle.net/1951/69914
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    • Mathematics Faculty Work [20]

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