关于函数图的固定数
On Fixing number of Functigraphs
摘要：
图$G$的固定数是它的顶点集$V(G)$的最小子集$S$的阶，使得$S$在$G$中的稳定子$Γ_{S}(G)$是平凡的.令$G_{1}$和$G_{2}$是图$G$的不相交副本，并且令$g:V(G_{1})\rightarrow V(G_{2})$是函数。函数图$F_{G}$由顶点集$V(G_{1})\cup V(G_{2})$和边集$E(G_{1})\cup E(G_{2})\cup \{uv:v=g(u)\}$组成。本文研究了固定数在从$G$到$F_{G}$的传递过程中的行为，并找到了固定数的精确上下界.我们还研究了一些著名的图族如完全图、树和联图的函数图的固定数。
英文摘要：
The fixing number of a graph $G$ is the order of the smallest subset $S$ of its vertex set $V(G)$ such that stabilizer of $S$ in $G$, $Γ_{S}(G)$ is trivial. Let $G_{1}$ and $G_{2}$ be disjoint copies of a graph $G$, and let $g:V(G_{1})\rightarrow V(G_{2})$ be a function. A functigraph $F_{G}$ consists of the vertex set $V(G_{1})\cup V(G_{2})$ and the edge set $E(G_{1})\cup E(G_{2})\cup \{uv:v=g(u)\}$. In this paper, we study the behavior of the fixing number in passing from $G$ to $F_{G}$ and find its sharp lower and upper bounds. We also study the fixing number of functigraphs of some well known families of graphs like complete graphs, trees and join graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
