Congratulations to

**Grace McCourt**, whose thesis has been added to the OhioLINK Electronic Theses & Dissertations Center. Grace's is the 34th Ashland University Honors Thesis to join the more than 90,000 dissertations and theses in the OhioLINK ETD Center.**Grace McCourt**presented a work entitled,

*The Dishonest Salesperson Problem.*“In graph theory, a graph is a set of vertices connected by edges. Consider a salesperson’s office that is located on a vertex v of a connected graph G with n vertices. There are n-1 customers located at each of the other vertices of the graph. The salesperson must make a driving trip whereby he or she leaves the office, visits each customer exactly once and then returns to the office. Because a profit is made on the mileage allowance, the salesperson wants to drive as far as possible during the trip, which financially benefits the salesperson at the loss of his or her employer, hence why the salesperson is being described as dishonest. …What is the maximum possible distance he or she can travel on such a trip, and how many different such trips are there? Problem 1654 from

*Mathematics Magazine*first posed and answered this question if the graph is a path graph, which represents the office and customers as equally spaced along a straight road.” Grace McCourt’s objective was to expand upon the result of Problem 1654 from

*Mathematics Magazine*using combinatorics and graph theory to derive results for the complete graph, in which each vertex is connected to each other vertex by exactly one edge, and the hypercube, which was defined in the presentation. McCourt also presented what was known for the cycle graph, the complete bipartite graph, and the complete m-ary tree of height h. Grace McCourt graduated May 2017 with a double major of Integrated Mathematics Education and Mathematics. Her URCA Faculty sponsor was Dr. Chris Swanson, a mathematics professor.

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