Two Rosa-type Labelings of Uniform k-distant Trees and a New Class of Trees

Authors

Kimberly Wenger Diller, Illinois Wesleyan UniversityFollow

Graduation Year

2015

Publication Date

Spring 2015

Comments

Faculty Advisor, Dr. Dan Roberts

Abstract

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 a, define app_a(G) to be the graph obtained from appending a leaves to each leaf in G. When G is a uniform k-distant tree, we show that app_a(G) admits both a graceful- and an α-labeling.

Disciplines

Discrete Mathematics and Combinatorics | Mathematics

Recommended Citation

Wenger Diller, Kimberly, "Two Rosa-type Labelings of Uniform k-distant Trees and a New Class of Trees" (2015). Honors Projects. 17.
https://digitalcommons.iwu.edu/math_honproj/17