A Closer Look at the Structure of Uniquely Pancyclic Graphs

Authors

Zak Kilpatrick, Louisiana Tech UniversityFollow

Document Type

Article

Publication Date

Spring 2024

Abstract

In this paper we will consider uniquely pancyclic graphs which are described as graphs on n vertices which have a unique cycle of size k for each integer k from 3 to n. To date, there are only seven known graphs of this type. To narrow down what a uniquely pancyclic graph could look like in order to aid the search in finding new ones, the focus of this paper is on the different ways the three and four cycles for these graphs can occur.

Recommended Citation

Kilpatrick, Zak, "A Closer Look at the Structure of Uniquely Pancyclic Graphs" (2024). Mathematics Senior Capstone Papers. 50.
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/50