论文标题
有限简单图和相关的有向图的重建猜想
The Reconstruction Conjecture for finite simple graphs and associated directed graphs
论文作者
论文摘要
在本文中，我们研究了有限简单图的重建猜想。让$γ$和$γ'$成为有限的简单图形，至少具有三个顶点，这样就存在一个$ f：v（γ）\ rightarrow v（γ'）$，对于任何v（γ）$中的任何$ v \，存在同组$ nistomorphism $ ϕ_v：v：γ-v \ tog tog togtomγ'f（v）$。然后，我们定义关联的有向图$ \widetildeγ= \widetildeγ（γ，γ'，f，f，\ {ϕ_v \} _ {v \ in V（γ）}）$，带有两种来自图形$γ$的箭头和$γ'$ f $ f $ f $ f $ f $ f $ f $ f $ f $ f。 $ \ {ϕ_V \} _ {v \ in V（γ）} $。通过研究相关的有向图$ \widetildeγ$，我们研究了两个图$γ$和$γ'$同构的何时。
In this paper, we study the Reconstruction Conjecture for finite simple graphs. Let $Γ$ and $Γ'$ be finite simple graphs with at least three vertices such that there exists a bijective map $f:V(Γ) \rightarrow V(Γ')$ and for any $v\in V(Γ)$, there exists an isomorphism $ϕ_v:Γ-v \to Γ'-f(v)$. Then we define the associated directed graph $\widetildeΓ=\widetildeΓ(Γ,Γ',f,\{ϕ_v\}_{v\in V(Γ)})$ with two kinds of arrows from the graphs $Γ$ and $Γ'$, the bijective map $f$ and the isomorphisms $\{ϕ_v\}_{v\in V(Γ)}$. By investigating the associated directed graph $\widetildeΓ$, we study when are the two graphs $Γ$ and $Γ'$ isomorphic.
