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Proceedings of the 2019 Undergraduate Mathematics Day

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This paper presents new ways to look at proving the Graceful Tree Conjecture, which was first posed by Kotzig, Ringel, and Rosa in 1967. In this paper, we will define an adjacency diagram for a graph, and we will use this diagram to show that several classes of trees are graceful.


Graceful labeling, trees




This paper was presented Saturday, Nov. 2, 2019, as part of Undergraduate Mathematics Day at the University of Dayton. Launched in 2003, Undergraduate Mathematics Day is held in odd-numbered years and alternates with the Biennial Alumni Career Seminar. The conference coincides with the annual Schraut Memorial Lecture, named Kenneth “Doc” Schraut, a mathematics faculty member from 1940 to 1978 and department chair from 1954 to 1970.

The 2019 Schraut lecturer was Tommy Ratliff, professor of mathematics at Wheaton College in Norton, Massachusetts, who presented the lecture “So How Do You Detect a Gerrymander?” His recent research hastaken up mathematical questions related to redistricting and gerrymandering, and he has been involved with the Metric Geometry and Gerrymandering Group based at Tufts University and Massachusetts of Technology.

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