Date of Award


Document Type


Degree Name

Master of Science (MS)


College of Science and Mathematics


Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Aihua Li

Committee Member

Jonathan Cutler

Committee Member

Baojun Song


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 cycle three graphs. I developed explicit formulas by implementing the toggling process to the graph. I further investigate the coefficients and special values of the interlace polynomial. Some of them can describe properties of the considered graph. Aigner and Holst also defined a new interlace polynomial, called the Q-interlace polynomial, recursively, which can tell other properties of the original graph. One immediate application of the Q-interlace polynomial is that a special value of it is the number of general induced subgraphs with an odd number of general perfect matchings. Thus by evaluating the Q-interlace polynomial at a specific value, we determine the number of general induced subrgaphs with an odd number of general perfect matchings of the considered Eulerian graph.

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Mathematics Commons