Regular maps from Cayley graphs III: t-balanced Cayley maps
Regular maps from Cayley graphs III: t-balanced Cayley maps
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DOI：
10.1016/j.disc.2005.09.042
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发表时间：
2007-02
期刊：
影响因子：
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通讯作者：
Lubica Liskova;M. Macaj;M. Škoviera
中科院分区：
文献类型：
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作者：
Lubica Liskova;M. Macaj;M. Škoviera
一类t-平衡Cayley映射[J]。Martino， M. Schultz，具有可解自同构群的对称Cayley映射，摘要于SIGMAC ' 98, Flagstaff， AR， 1998]是Širáň和Škoviera引入并研究的平衡和反平衡Cayley映射的自然推广[来自Cayley图的正则映射II：反平衡Cayley映射，离散数学，124 (1994)179-191；群的符号结构及其反自同构，离散数学，108(1992)189-202。本文通过研究t平衡Cayley映射的逆、自同构群和指数的分布来继续这一研究。这些方法是基于使用带符号结构群的t自同构，它扩展了反自同构的概念，对反平衡Cayley映射至关重要。作为应用，对每一个能被8整除的n构造了一系列完全二部图Kn，nis的非标准正则嵌入。
The class of t-balanced Cayley maps [J. Martino, M. Schultz, Symmetrical Cayley maps with solvable automorphism groups, abstract in SIGMAC ’98, Flagstaff, AR, 1998] is a natural generalisation of balanced and antibalanced Cayley maps introduced and studied by Širáň and Škoviera [Regular maps from Cayley graphs II: antibalanced Cayley maps, Discrete Math. 124 (1994) 179–191; Groups with sign structure and their antiautomorphisms, Discrete Math. 108 (1992) 189–202]. The present paper continues this study by investigating the distribution of inverses, automorphism groups, and exponents of t-balanced Cayley maps. The methods are based on the use of t-automorphisms of groups with sign structure which extend the notion of an antiautomorphism crucial for antibalanced Cayley maps. As an application, a new series of nonstandard regular embeddings of complete bipartite graphs Kn,nis constructed for each n divisible by 8.