t-Balanced Cayley maps of dihedral groups |
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| Institution: | 1. Department of Automation, Tsinghua University, Beijing 100084, China;2. Department of Physics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;1. Faculdade de Formação de Professores, Universidade do Estado do Rio de Janeiro, Brazil;2. Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Brazil;3. CNRS, GeoD research group, “Maths à modeler” project, Laboratoire Leibniz, France;4. Departamento de Informática, Universidade Estadual de Maringá, Brazil;5. Instituto de Computação, Universidade Estadual de Campinas, Brazil;1. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, People’s Republic of China;2. Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China |
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| Abstract: | A Cayley map is an embedding of a Cayley graph where the cyclic ordering of generators around every vertex is the same. The involution indicating the position of mutually inverse generators in the cyclic ordering is called the distribution of inverses of a Cayley map. The Cayley maps whose distribution of inverses is linear (modulo the degree of the map) with 'slope' t are called t-balanced. An exponent of a Cayley map is a number e with the property that, roughly speaking, the Cayley map is isomorphic to its 'e-fold rotational image'.In the contribution we present results related to the construction of t-balanced Cayley maps which are not regular and do not have t as an exponent. |
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