广义Petersen图$P_{2,7}$的边传递性

Edge Transitivity of the Generalized Petersen Graph $P_{2,7}$

摘要: 广义Petersen图$P_{k,n}$ 是一种在图论中具有重要研究价值的正则图，其独特的对称性与复杂的结构特性使其在图论中具有广泛的应用价值。文章以广义Petersen图中的$P_{2,7}$ 为研究对象，通过深入分析其顶点构造与自同构群的特性，结合严格的理论推导，详细证明了$P_{2,7}$ 并非边传递图。

Abstract: The generalized Petersen graph $P_{k,n}$ is a class of regular graphs with significant research value in graph theory. Its unique symmetry and complex structural properties make it widely applicable in various areas of graph theory. This paper focuses on the generalized Petersen graph $P_{2,7}$ , conducting an in-depth analysis of its vertex construction and automorphism group. Through rigorous theoretical derivation, it is demonstrated in detail that $P_{2,7}$ is not edge-transitive, providing new theoretical insights into the study of symmetry and transitivity in generalized Petersen graphs.