Title: Tree Expressions and Graph Tilings
 
Abstract: 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.