论文标题
图和完整骨架中的结构等效性
Structural Equivalence in Graphs and Complete Skeletons
论文作者
论文摘要
且仅当thructions $ u $ $ u $和$ v $ c $γ$在且仅当threstosition $（u \ \，v）$中含量等于抗曲线（$γ$）（$γ$），即$γ$的自动形态组。讨论了结构对等的某些属性和由AUT中的换位（$γ$）产生的顶点排列的组，以及这些组的主要图。结构等效性的概念用于开发一种将图形重新配置为所谓的完整骨架的方法，该骨架与压缩图密切相关。最后，图$γ$（表示为$ω（γ）$）的完整骨架用于寻找级别$（i+a（γ））$的公式，这有助于确定-1欧元值$γ$。
Two vertices $u$ and $v$ of a graph $Γ$ are strucuturally equivalent if and only if the transposition $(u\,v)$ is in Aut($Γ$), the automorphism group of $Γ$. Some properties of structural equivalence and the group of vertex permutations generated by the transpositions in Aut($Γ$) are discussed, along with the prime graphs of these groups. The notion of structural equivalence is used to develop a way of reconfiguring graphs into what are called their complete skeletons, which is closely related to compression graphs. Finally, the complete skeleton of a graph $Γ$, denoted $Ω(Γ)$, is used to find a formula for rank$(I+A(Γ))$, which is helpful for determining the multiplicity of the -1 eigenvalue of $Γ$.
