How to draw many semi-circles in a row with different centres in Tikz

Question

I am wanting to draw five semi-circles in a row (something like the second photo). This is a graph with the dots as vertices/nodes. I can draw one semi-circle, which is centered at the origin (pleae see first photo) and this is exactly what I want them to look like, but I can't duplicate it at centres (-6;0), (-12;0), (6;0) and (12;0). How do I draw the other 4?

I attach my LateX code.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,decorations.pathmorphing,backgrounds,positioning,fit,petri,calc,graphs,graphs.standard}
\begin{document}
 \begin{figure}[h]
    \begin{center}
        \begin{tikzpicture}
            [scale=0.6,inner sep=0.5mm, % this is the node radius
            vertex/.style={circle,draw}, % this defines the default style for the vertex class
            thickedge/.style={line width=2pt}] % this defines the default style for the thick edges

            \def\r{3} 

            \foreach \point in {(0:\r) ,(90:\r),(180:\r),(60:\r),(30:\r),(150:\r),(120:\r)} 
            \draw[fill=white] \point circle(.12);
            \node at (60:\r) {} ;
            \node at (30:\r) {} ;
            \node at (150:\r) {} ;
            \node at (120:\r) {} ;


            \node[vertex] (1) at (0,0) [fill=white] {};
            \node[vertex] (2) at (0,3) [fill=white] {};
            \node[vertex] (3) at (-3,0) [fill=white] {};
            \node[vertex] (5) at (3,0) [fill=white] {};

            \draw (1)--(2);
            \draw (3)--(1)--(5);

            \draw (0,0)+(122:3cm) arc[start angle=122, end angle=148, radius=3cm];
            \draw (0,0)+(32:3cm) arc[start angle=32, end angle=58, radius=3cm];
            \draw (0,0)+(28:3cm) arc[start angle=28, end angle=2, radius=3cm];
            \draw (0,0)+(-182:3cm) arc[start angle=-182, end angle=-208, radius=3cm];
            \draw  (0,0)+(-242:3cm) arc[start angle=-242, end angle=-268, radius=3cm];
            \draw  (0,0)+(-272:3cm) arc[start angle=-272, end angle=-298, radius=3cm];
        \end{tikzpicture}
    \end{center}
\end{figure}

\end{document}

Answer 1

Welcome to TeX.SE

I think you're looking for something like this, using a couple of \foreach loops to repeat semicircles and points:

\documentclass[tikz,border=1.618]{standalone}
\begin{document}
\begin{tikzpicture}
\foreach\i in {0,2,...,8}
{
  \draw (\i,0) arc (180:0:1) -- cycle;
  \foreach\j in {0,30,60,...,180}
    \fill (\i+1,0) ++  (\j:1) circle (1pt);
  \draw (\i+1,0) --++ (0,1);
  \fill (\i+1,0) circle (1pt);
}
\end{tikzpicture}
\end{document}

Update (white nodes): In this case we need to draw the lines before the nodes:

\documentclass[tikz,border=1.618]{standalone}
\begin{document}
\begin{tikzpicture}
\foreach\i in {0,2,...,8}
{
  \draw (\i,0) arc (180:0:1) -- cycle;
  \draw (\i+1,0) --++ (0,1); % <-- before the nodes
  \foreach\j in {0,30,60,...,180}
    \draw[black,fill=white] (\i+1,0) ++  (\j:1) circle (1pt);
  \draw[black,fill=white] (\i+1,0) circle (1pt);
}
\end{tikzpicture} 
\end{document}

Answer 2

Just for fun let's do it with pic. more details about pic are here. The short version is that it is a tikz code fragment that you can predefine and reuse really easily. as Juan Castaño said : "That said, a \pic could make the semicircle more customizable: sizes, rotations, colors,". You can more by doing less. Here is the code:

\documentclass[border=1.618]{standalone}
\usepackage{tikz}
\begin{document}
    \begin{tikzpicture}[
         semicircles/.pic={ 
            \draw (0,0) arc (180:0:#1) -- cycle;
            \foreach\j in {0,30,60,...,180}
                \fill (#1,0) ++  (\j:#1) circle (1pt);
            \draw (#1,0) --++ (0,#1);
            \fill (#1,0) circle (1pt);
        }

    ]
    \foreach \j in {0,2,...,8}{
        \pic  at (\j,0){semicircles=1};
        \pic  [rotate=45,yshift=5cm] at (\j,0){semicircles=2};
    }
\end{tikzpicture}
\end{document}

Here is the result.

Edit: With Juan Castaño's suggestion, we can add a pic actions which are style option that can only be deployed in a pic.

The usefulness stems from the ability of adding arbitrary style and let's us transmit <key>=<value> argument to change the style of some content of the pic.

from the last code, all that we change is

\fill (#1,0) circle (1pt);

into

\fill [pic actions] (#1,0) circle (1pt);

Which means that now any call to this pic can change the circle's style like this:

``

\begin{tikzpicture}[
     semicircles/.pic={ 
        \draw (0,0) arc (180:0:#1) -- cycle;
        \foreach\j in {0,30,60,...,180}
            \fill (#1,0) ++  (\j:#1) circle (1pt);
        \draw (#1,0) --++ (0,#1);
        \fill [pic actions] (#1,0) circle (1pt);
        }   
    ]
    \foreach \j in {0,2,...,8}{
        \pic  at (\j,0){semicircles=1};
        \pic  [rotate=45,yshift=5cm] at (\j,0){semicircles=2};
        \pic [fill=red] at (\j,-2){semicircles=1};
    }
\end{tikzpicture}