I have drawn these diagrams, but need help with broken circles around the right-hand bullet using tikz-cd

Question

\documentclass{amsart}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{tikz-cd}
\usepackage{mathtools,amscd}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{babel}
\usepackage{dynkin-diagrams}
\usetikzlibrary{backgrounds}
\begin{document}
\begin{enumerate}

\item[]$\widehat{L_2}$

\item[]$\begin{tikzcd}[column sep=small,row sep=small]
\widehat{K_3} & \bullet \arrow[rr, no head, bend left] \arrow[rr, no head, bend right] \arrow[rr, no head] &  & \bullet
\end{tikzcd}$

\item[]$\begin{tikzcd}[column sep=small,row sep=small]
              & \bullet \arrow[rrrrdd, no head] &  & \bullet \arrow[rrdd, no head] &  & \bullet \arrow[dd, no head] &  & \bullet \arrow[lldd, no head] &  & \bullet \arrow[lllldd, no head] \\
\widehat{S_5} &                                 &  &                               &  &                             &  &                               &  &                                 \\
              &                                 &  &                               &  & \bullet                     &  &                               &  &
\end{tikzcd}$

\item[]$\begin{tikzcd}
\widehat{A_0} & \bullet \arrow[out=150,in=210,loop,no head]
\arrow[r, no head]&\bullet
\end{tikzcd}$

\item[]$\begin{tikzcd}[column sep=small,row sep=small]
\widehat{A_1} & \bullet \arrow[rr, no head, bend left] \arrow[rr, no head, bend right] &  & \bullet \arrow[rr, no head] &  & \bullet
\end{tikzcd}$

\item []$\begin{tikzcd}[column sep=small,row sep=small]
              & \bullet \arrow[dd, no head] \arrow[rrd, no head] &  &                             &  &         \\
\widehat{A_2} &                                                  &  & \bullet \arrow[rr, no head] &  & \bullet \\
              & \bullet \arrow[rru, no head]                     &  &                             &  &
\end{tikzcd}$

\item []$\begin{tikzcd}[column sep=small,row sep=small]
              &                                                 & \bullet \arrow[rd, no head] &                             &  &         \\
\widehat{A_3} & \bullet \arrow[ru, no head] \arrow[rd, no head] &                             & \bullet \arrow[rr, no head] &  & \bullet \\
              &                                                 & \bullet \arrow[ru, no head] &                             &  &
\end{tikzcd}$

\item []$\begin{tikzcd}[column sep=small,row sep=small]
              & \bullet \arrow[rr, no head] \arrow[dd, no head] &  & \bullet \arrow[rrd, no head] &  &                             &  &         \\
\widehat{A_4} &                                                 &  &                              &  & \bullet \arrow[rr, no head] &  & \bullet \\
              & \bullet \arrow[rr, no head]                     &  & \bullet \arrow[rru, no head] &  &                             &  &
\end{tikzcd}$

\item[]$\begin{tikzcd}[column sep=small,row sep=small]
              &                                                 & \bullet \arrow[rr, no head] &  & \bullet \arrow[rd, no head] &                             &  &         \\
\widehat{A_5} & \bullet \arrow[ru, no head] \arrow[rd, no head] &                             &  &                             & \bullet \arrow[rr, no head] &  & \bullet \\
              &                                                 & \bullet \arrow[rr, no head] &  & \bullet \arrow[ru, no head] &                             &  &
\end{tikzcd}$

\item[]$\begin{tikzcd}[column sep=small,row sep=small]
              & \bullet \arrow[rr, no head] \arrow[dd, no head] &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rrd, no head] &  &                             &  &         \\
\widehat{A_6} &                                                 &  &                             &  &                              &  & \bullet \arrow[rr, no head] &  & \bullet \\
              & \bullet \arrow[rr, no head]                     &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rru, no head] &  &                             &  &
\end{tikzcd}$

\item[]$\begin{tikzcd}[column sep=small,row sep=small]
              & \bullet \arrow[rd, no head] &                                                 & \bullet \arrow[rr, no head] &  & \bullet \\
\widehat{D_4} &                             & \bullet \arrow[rd, no head] \arrow[ru, no head] &                             &  &         \\
              & \bullet \arrow[ru, no head] &                                                 & \bullet                     &  &
\end{tikzcd}$

\item[]$\begin{tikzcd}[column sep=small,row sep=small]
              & \bullet \arrow[rrd, no head] &  &                             &  &                                                   &  & \bullet \arrow[rr, no head] &  & \bullet \\
\widehat{D_5} &                              &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rru, no head] \arrow[rrd, no head] &  &                             &  &         \\
              & \bullet \arrow[rru, no head] &  &                             &  &                                                   &  & \bullet                     &  &
\end{tikzcd}$

\item[]$\begin{tikzcd}[column sep=small,row sep=small]
              & \bullet \arrow[rrd, no head] &  &                             &  &                             &  &                                                   &  & \bullet \arrow[rr, no head] &  & \bullet \\
\widehat{D_6} &                              &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rru, no head] \arrow[rrd, no head] &  &                             &  &         \\
              & \bullet \arrow[rru, no head] &  &                             &  &                             &  &                                                   &  & \bullet                     &  &
\end{tikzcd}$

\item[]$\begin{tikzcd}[column sep=small,row sep=small]
              & \bullet \arrow[rrd, no head] &  &                             &  &                             &  &                             &  &                                                   &  & \bullet \arrow[rr, no head] &  & \bullet \\
\widehat{D_7} &                              &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rru, no head] \arrow[rrd, no head] &  &                             &  &         \\
              & \bullet \arrow[rru, no head] &  &                             &  &                             &  &                             &  &                                                   &  & \bullet                     &  &
\end{tikzcd}$

\item[]$\begin{tikzcd}[column sep=small,row sep=small]
              & \bullet \arrow[rrd, no head] &  &                             &  &                             &  &                             &  &                             &  &                                                   &  & \bullet \arrow[rr, no head] &  & \bullet \\
\widehat{D_8} &                              &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rr, no head] &  & \bullet \arrow[rru, no head] \arrow[rrd, no head] &  &                             &  &         \\
              & \bullet \arrow[rru, no head] &  &                             &  &                             &  &                             &  &                             &  &                                                   &  & \bullet                     &  &
\end{tikzcd}$


\item[]$\begin{tikzcd}
              &                            &                            & \bullet \arrow[d, no head] &                            &                            &         \\
              &                            &                            & \bullet \arrow[d, no head] &                            &                            &         \\
\widehat{E_6} & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \circ
\end{tikzcd}$

\item[]$\begin{tikzcd}
              &                            &                            &                            & \bullet \arrow[d, no head] &                            &                            &                            &       \\
\widehat{E_7} & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \circ
\end{tikzcd}$

\item[]$\begin{tikzcd}
              &                            &                            & \bullet \arrow[d, no head] &                            &                            &                            &                            &                            &       \\
\widehat{E_8} & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \bullet \arrow[r, no head] & \circ
\end{tikzcd}$


\end{enumerate}
\end{document} 

I draw the following diagrams, but do you help me write the open circles around the right-most bullet by using tikz-cd? and Can I make the L_2 loop diagram using tikz-cd?

Answer 1

One method would be to add

\tikzset{
  OpenCirc/.style={
    label={[inner sep=0,minimum size=10mm, circle, draw, densely dotted]center:{}}
    }
}

to the preamble, and add |[OpenCirc]| to the start of the cells where you want the bullet circled. E.g.

... & |[OpenCirc]| \bullet \arrow[llldd, no head] 

By the way, if you want the lines to reach the bullets, then you could define

Bullet/.style={
  circle, fill, draw, inner sep=0, minimum size=4pt
  }

and use |[Bullet]| instead of \bullet in the cells. For a bullet with a circle, use |[Bullet, OpenCirc]|.

Regarding your other question, you could do

\begin{tikzpicture}
 \node [Bullet] (a) {};
 \draw (a)
     arc[start angle=0,end angle=360,radius=5mm]
     arc[start angle=0,end angle=360,radius=8mm];
\end{tikzpicture}

with the Bullet style defined above.

Here is a complete example:

\documentclass{amsart}
\usepackage{tikz-cd}
\tikzset{
  OpenCirc/.style={
    label={[inner sep=0,minimum size=10mm, circle, draw, densely dotted]center:{}}
    },
  Bullet/.style={
    circle, fill, draw, inner sep=0, minimum size=4pt
    }
}
\begin{document}
$\begin{tikzcd}[column sep=small,row sep=small]
              & |[Bullet]| \arrow[rrrrdd, no head] &  & |[Bullet]| \arrow[rrdd, no head] &  & |[Bullet]| \arrow[dd, no head] &  & |[Bullet]| \arrow[lldd, no head] &  & |[OpenCirc, Bullet]| \arrow[lllldd, no head] \\
\widehat{S_5} &                                    &  &                                  &  &                                &  &                                  &  &                                 \\
              &                                    &  &                                  &  & |[Bullet]|                     &  &                                  &  &
\end{tikzcd}$

\begin{tikzpicture}
 \node [Bullet] (a) {};
 \draw (a)
     arc[start angle=0,end angle=360,radius=5mm]
     arc[start angle=0,end angle=360,radius=8mm];
\end{tikzpicture}
\end{document}