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Interlace Polynomial of a Special Eulerian Graph

April 24, 2015, 12:00 pm
Location Richardson Hall - 224A
Posted InCollege of Science and Mathematics

Abstract

In a recent paper, Arratia, Bollobas and Sorkin discussed a graph polynomial defined recursively, which they call the interlace polynomial. There have been previous results on the interlace polynomials for special graphs, such as paths, cycles, and trees. Applications have been found in biology and other areas. In this research, I focus on the interlace polynomial of a special type of Eulerian graph, built from one cycle of size n and n triangles. For such a graph, my goal is to develop recursive and explicit formulas for the interlace polynomial. I will show that by implementing the toggling process to our graph, explicit formulas can be obtained. Aigner and Holst also defined a new interlace polynomial recursively, which holds a few di fferent properties from their original. In this paper, I will develop the recursive and explicit formulas for this new interlace polynomial as well. These explicit formulas provide me the opportunity to discuss several properties within the graph. Also, the formulas can be applied to other fields of study.