Mathematics Commons^™

Two Rosa-Type Labelings Of Uniform K-Distant Trees And A New Class Of Trees, Kimberly Wenger Diller

Honors Projects

A k-distant tree consists of a main path, called the spine, such that each vertex on the spine is joined by an edge to an end-vertex of at most one path on at most k vertices. Those paths, along with the edge joining them to the spine, are called tails. When every vertex on the spine has exactly one incident tail of length k we call the tree a uniform k-distant tree. We show that every uniform k-distant tree admits both a graceful- and an α-labeling.

For a graph G and a positive integer …

Path-Tables Of Trees: A Survey And Some New Results, Kevin Asciak

Theory and Applications of Graphs

The (vertex) path-table of a tree Τ contains quantitative information about the paths in Τ. The entry (i,j) of this table gives the number of paths of length j passing through vertex ^vi. The path-table is a slight variation of the notion of path layer matrix. In this survey we review some work done on the vertex path-table of a tree and also introduce the edge path-table. We show that in general, any type of path-table of a tree Τ does not determine Τ uniquely. We shall show that in trees, the number of paths passing through …