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