"Automorphism" 是一个术语，通常用于数学和计算机科学中，特别是在群论和图论中。它指的是一个变换，这种变换保持了对象的结构不变。例如，在群论中，一个群G的自同构就是G上的一个automorphism。
以下是一篇关于automorphism的英文范文，供您参考：
Automorphisms of Groups
In mathematics, automorphisms are transformations that preserve the structure of an object. In group theory, for example, an automorphism of a group G is a bijective function φ : G → G that preserves the properties of G, such as inverses and composition of elements.
One of the most important properties of automorphisms is that they act transitively on the elements of the group, meaning that if g1 and g2 are two elements of the group, there exists an automorphism φ that maps g1 to g2. This property allows us to study groups using their automorphisms, which can provide valuable insights into the structure and properties of the group.
Another important application of automorphisms is in graph theory, where they can be used to study the symmetry and structure of graphs. In particular, automorphisms of a graph can be used to identify equivalent classes of graphs, and to study properties such as connectivity and edge-connectivity.
In summary, automorphisms are a powerful tool in the study of groups and graphs, providing insights into their structure and properties. Understanding automorphisms can be helpful in developing new algorithms and designing efficient algorithms for graph-based problems.
automorphism是一个英文单词，翻译为“自同态”或“自同构”。
在英文范文中的应用举例：在群论中，一个群G的自同态就是满足自映射性质的群元素，即群元素G的映射f是G到自身的同态映射。
以上信息仅供参考，如需更多信息，可以到英语文章网站查询。
"Automorphism"是一个术语，通常用于数学和计算机科学中，特别是在群表示理论和图论中。它指的是一个变换，这种变换保持了对象的结构不变。
在英文中，"automorphism"的最新变化可能没有特别显著的变化，因为它是一个相对稳定的术语。然而，随着时间的推移，这个词可能会在新的上下文中出现，以适应新的研究领域或技术。
以下是一个automorphism的英文范文示例：
Automorphisms of Graphs: A Survey
In this paper, we will discuss the concept of automorphisms in graphs, their classification, and their applications in various areas of graph theory and computer science. Specifically, we will focus on the study of automorphisms of graphs, which are transformations that preserve the structure of the graph without changing its shape. These transformations can be used to study the symmetry and structure of graphs, and they have been extensively studied in recent years. We will also discuss some of the classification schemes for automorphisms of graphs, as well as their applications in various areas such as graph coloring, graph recognition, and more.
希望这个示例能帮助你理解automorphism在英文中的用法和最新变化。如果你有更具体的问题或需要更多的帮助，请随时告诉我！