论文标题
涉及顶点传递图的图形对的稳定性
Stability of graph pairs involving vertex-transitive graphs
论文作者
论文摘要
如果$γ\times点$γ\times点$γ\ timephist组为$γ$和$γ$和$σ$且不稳定的产品，则一对图$（γ，σ）$是稳定的，否则$γ\γ\γ\ fimepimemγ\\ timepientpient $γ$是$γ$和$γ$和$ fightable和$γ$。在本文中，我们将带有cocrime valencies的任何一对常规图$（γ，σ）$的稳定性和顶点传播$σ$减少了$（γ，k_2）$的稳定性。由于文献中对后者进行了充分的研究，因此，在$σ$是$σ$是pertex-transitve和$（γ，k_2）$的稳定性的情况下，我们能够确定任何一对常规图$（γ，σ）$的稳定性。
A pair of graphs $(Γ,Σ)$ is said to be stable if the full automorphism group of $Γ\timesΣ$ is isomorphic to the product of the full automorphism groups of $Γ$ and $Σ$ and unstable otherwise, where $Γ\timesΣ$ is the direct product of $Γ$ and $Σ$. In this paper, we reduce the study of the stability of any pair of regular graphs $(Γ,Σ)$ with coprime valencies and vertex-transitive $Σ$ to that of $(Γ,K_2)$. Since the latter is well studied in the literature, this enables us to determine the stability of any pair of regular graphs $(Γ,Σ)$ with coprime valencies in the case when $Σ$ is vertex-transitve and the stability of $(Γ,K_2)$ is known.
