AI 中文总结
研究图的顶点传递闭包及顶点传递数，运用代数和组合方法，确定使得图存在正则顶点传递闭包的最小整数，为相关研究提供方法与结论。
AI 中文摘要
图\(\Gamma\)的顶点传递闭包是在相同顶点集上\(\Gamma\)的顶点传递超图。图\(\Gamma\)的顶点传递数记为\(d_{vt}(\Gamma)\)，是使得存在\(\Gamma\)的\(d_{vt}(\Gamma)\) - 正则顶点传递闭包的最小整数。本文用多种代数和组合方法研究图的顶点传递闭包及相关顶点传递数。
英文摘要
A vertex-transitive closure of $Γ$ is a vertex-transitive supergraph of $Γ$ on the same vertex set. The vertex-transitive number of a graph $Γ$, denoted by $d_{vt}(Γ)$, is the smallest integer for which there exists a $d_{vt}(Γ)$-regular vertex-transitive closure of $Γ$. In this paper we use various algebraic and combinatorial methods to study vertex-transitive closures of graphs and the associated vertex-transitive number.
Comments8 pages, 3 figures
