Odd extensions of transitive groups via symmetric graphs – The cubic case
Odd extensions of transitive groups via symmetric graphs – The cubic case
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通过对称图的传递群的奇扩展 — 立方情况
DOI：
10.1016/j.jctb.2018.10.003
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Dragan Marušič
中科院分区：
文献类型：
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作者：
Klavdija Kutnar;Dragan Marušič
在处理数学对象的对称性时，一个基本问题是确定它们的全自同构群。在本文中，这个问题被认为是在上下文中的偶/奇排列二分法。更确切地说：当存在的自同构充当图的顶点集上的偶置换，称为even自同构，迫使存在的自同构充当奇置换，称为dodd自同构。作为解决上述问题的第一步，给出了关于三次对称图中奇自同构存在性的完整信息。
When dealing with symmetry properties of mathematical objects, one of the fundamental questions is to determine their full automorphism group. In this paper this question is considered in the context of even/odd permutations dichotomy. More precisely: when is it that the existence of automorphisms acting as even permutations on the vertex set of a graph, calledeven automorphisms, forces the existence of automorphisms that act as odd permutations, calledodd automorphisms. As a first step towards resolving the above question, complete information on the existence of odd automorphisms in cubic symmetric graphs is given.