Publication Date

Spring 2018

Advisor(s) - Committee Chair

Dr. Dominic Lanphier (Director), Dr. Attila Por, and Dr. Claus Ernst

Degree Program

Department of Mathematics

Degree Type

Master of Science


A labeling of a graph is an assignment of a natural number to each vertex

of a graph. Graceful labelings are very important types of labelings. The study of graceful labelings is very difficult and little has been shown about such labelings. Vertex-relaxed graceful labelings of graphs are a class of labelings that include graceful labelings, and their study gives an approach to the study of graceful labelings. In this thesis we generalize the congruence approach of Rosa to obtain new criteria for vertex-relaxed graceful labelings of graphs. To do this, we generalize Faulhaber’s Formula, which is a famous result about sums of powers of integers.


Discrete Mathematics and Combinatorics | Mathematics