Review
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Automorphism Group of Polyhedral Graphs
Version 1
: Received: 22 December 2023 / Approved: 25 December 2023 / Online: 25 December 2023 (15:57:27 CET)
A peer-reviewed article of this Preprint also exists.
Ghorbani, M.; Alidehi-Ravandi, R.; Dehmer, M. Automorphism Groups in Polyhedral Graphs. Symmetry 2024, 16, 1157. Ghorbani, M.; Alidehi-Ravandi, R.; Dehmer, M. Automorphism Groups in Polyhedral Graphs. Symmetry 2024, 16, 1157.
Abstract
Symmetry, as a key concept in geometry and the foundational principle of mathematical concepts, is a fundamental part of geometry and nature, creating patterns that help us conceptually organize our world. It is often linked with aesthetic beauty and can be observed in both natural phenomena and human-made objects, such as artworks and manufactured products, across the globe. The automorphism group of a graph is a mathematical structure that captures all the symmetries of the graph. symmetry refers to the property of a graph, indicating that it can be transformed without changing its structure, while the automorphism group is the collection of all permutations of the vertices that preserve the graph's adjacency relationships. In graph theory, the concepts of symmetry group and automorphism group play fundamental roles in understanding the symmetries and structural properties of graphs. This paper aims to explore the relationship between symmetry groups and automorphism groups, shedding light on their interconnected nature and their significance in graph theory. We delve into the definitions and properties of both symmetry groups and automorphism groups, highlighting their similarities and distinctions. Furthermore, we discuss their applications in various fields, including computer science, chemistry, and network analysis. Through this exploration, we aim to provide a comprehensive understanding of the relationship between symmetry groups and automorphism groups, deepening our comprehension of the symmetries and structures inherent in graphs.
Keywords
symmetry; automorphism group; polyhedral graph; fullerene
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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