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Symmetric Colorings of the Hypercube and Hyperoctahedron

Phillips, Bo
http://rave.ohiolink.edu/etdc/view?acc_num=wright1460642665

Abstract Details

2016, Master of Science (MS), Wright State University, Mathematics.
A self-complementary graph G is a subgraph of the complete graph K_n that is isomorphic to its complement. A self-complementary graph can be thought of as an edge 2-coloring of K_n that admits a color-switching automorphism. An automorphism of K_n that is color-switching for some edge 2-coloring is called a complementing automorphism. Complementing automorphisms for K_n have been characterized in the past by such authors as Sachs and Ringel. We are interested in extending this notion of self-complementary to other highly symmetric families of graphs; namely, the hypercube Q_n and its dual graph, the hyperoctahedron O_n. To that end, we develop a characterization of the automorphism group of these graphs and use it to prove necessary and sufficient conditions for an automorphism to be complementing. Finally, we use these theorems to construct a computer search algorithm which finds all self-complementary graphs in Q_n and O_n up to isomorphism for n=2,3,4.
Daniel Slilaty, Ph.D. (Advisor)
Yuqing Chen, Ph.D. (Committee Member)
Xiangqian Zhou, Ph.D. (Committee Member)
48 p.
Mathematics
mathematics

Recommended Citations

Citations

  • Phillips, B. (2016). Symmetric Colorings of the Hypercube and Hyperoctahedron [Master's thesis, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright1460642665

    APA Style (7th edition)

  • Phillips, Bo. Symmetric Colorings of the Hypercube and Hyperoctahedron. 2016. Wright State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=wright1460642665.

    MLA Style (8th edition)

  • Phillips, Bo. "Symmetric Colorings of the Hypercube and Hyperoctahedron." Master's thesis, Wright State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=wright1460642665

    Chicago Manual of Style (17th edition)

wright1460642665
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© 2016, all rights reserved.
This open access ETD is published by Wright State University and OhioLINK.