Mathematics and Statistics
Washington State University
Tree Expressions and Graph Tilings
We consider “tree expressions,”
obtained as quotients of determinants of generalized
Laplacian matrices of trees. For a specific example of
the structures provided by tree expressions, this
computation applied to paths yields a standard
continued fraction structure.
As an application, we will examine how tree
expressions arise in “graph tilings,” obtained by
covering each edge of a graph together with zero, one,
or two of its endpoints so that every vertex is
accounted for exactly once in the tiling.