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Pure Mathematics 2025
一类奇数阶4度非2-弧传递图的构造
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Abstract:
本文是在图的阶为奇数，度数为4的条件下，通过分析图
的自同构群的子群及其点稳定子群的结构，特别是弧传递图的相关理论和基本性质，利用特定顶点和度数的群的作用和图的对称性等相关理论，进一步探讨了这类图的存在性和结构特征，给出了一类奇数阶4度非2-弧传递图的构造。
In this paper, under the condition of odd order and degree 4. By analyzing the structure of subgroups of the automorphism group of the graph and its point-stabilizer subgroups, especially relying on the relevant theories and basic properties of arc-transitive graphs, and making use of the group actions on specific vertices and degrees, as well as the theories related to the symmetry of the graph, the existence and structural characteristics of such graphs are further explored. A construction method for a class of odd-order 4-degree non-2-arc-transitive graphs is presented.
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