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#### Project Title

Vertex-Magic Graphs

#### Abstract/Description

In graph theory, a graph labeling is an assignment of labels to the edges and vertices of a graph. There are many different types of graphs labelings. Some include graceful labelings, harmonious labelings, and magic labelings. In this project we will focus on a type of magic labeling. A vertex-magic total labeling is a labeling such that the vertices and edges are assigned consecutive integers between 1 and v+e, where v is the order of the graph and e is the size of the graph. When the sum of the labels of a vertex and its incident edges results in the same integer for each vertex, we have a vertex-magic total labeling. This integer is called the magic number of the graph and the graph is called a vertex-magic graph. There has been previous research on vertex-magic total labelings and we know a lot about certain classes of graphs. In this project, we are considering crown graphs. We will give upper and lower bounds of the magic number, a function that generates vertex-magic total labelings of crown graphs and discuss other results about this kind of labeling.

#### Note on the Author

Karissa Massud is a graduating senior double majoring in Mathematics and Secondary Education and double minoring in Statistics and Spanish. Her research project was completed in the summer of 2021, which in turn supported the completion of her thesis in the fall, all under the mentorship of Dr. Shannon Lockard (Mathematics). Karissa’s research was made possible with funding provided by the Adrian Tinsley Program (ATP) grant for undergraduate research. Karissa will present this work at the 2022 Mathematical Association of America’s (MAA) MathFest and the 2022 National Conference on Undergraduate Research (NCUR). She plans to pursue a Ph.D. in Pure Mathematics and begin teaching after graduation.

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