绘制无交叉顶点的曲线

Question

我正在尝试绘制下图，但在绘制曲线和虚线时遇到了困难。

有谁能够帮助我？

            \begin{tikzpicture}[scale = 0.75]
                
                \tikzset{roundnode/.style={thick, draw = black, fill = white, outer sep = 1.5, circle, minimum size = 10pt, scale = 0.75}}
                
                \node[roundnode = black] (1) at (30, 2.01){$v_1$};
                \node[roundnode = black] (2) at (31.91, 0.62){$v_2$};
                \node[roundnode = black] (3) at (31.18, -1.63){$v_3$};
                \node[roundnode = black] (4) at (28.82, -1.63){$v_4$};
                \node[roundnode = black] (5) at (28.09, 0.62){$v_5$};
                \node[roundnode = black] (6) at (30, -0.1){$v$};
                
                
                
                \draw
                (1) edge[-,thick]   (6)
                (2) edge[-,thick]   (6)
                (3) edge[-,thick]   (6)
                (4) edge[-,thick]   (6)
                (5) edge[-,thick]   (6)
                %(3) edge[-,thick]   (4)
                ;
            \end{tikzpicture}

Answer 1

\documentclass[tikz,border=2mm]{standalone}
\begin{document}
\begin{tikzpicture}[roundnode/.style={thick, 
    draw = black, fill = white, outer sep = 1.5, circle,
     minimum size = 2em}]
 \draw (0,0) node[roundnode,dashed](0){$v$}
   foreach \x [evaluate=\x as \y using {144-72*\x}] in {1,...,5}
  {(\y:2) node[roundnode,label={\y+90:{$\x$}}](\x){$v_{\x}$}
   edge (0)
  }
  [shift={(4,0)}]
     foreach \z [count=\x,evaluate=\x as \y using {180-72*\x}] in {3,1,3,1}
  {(\y:2) node[roundnode,label={\y:{$\z$}}](p\x){}
   \ifnum\x=1
    edge[dashed] (1)
   \else
    edge[dashed] (p\the\numexpr\x-1)
   \fi
  } (p4) edge[dashed] (3);
\end{tikzpicture}
\end{document}

Answer 2

您可以在此处使用极坐标和范围，这将使定位节点和编写代码变得更加容易。我添加了一个标签，以防您想标记节点。您可以使用该bend选项制作一条简单的曲线。

你想要这样的东西吗？

\documentclass[border=10pt,tikz]{standalone}

\begin{document}

\begin{tikzpicture}[
    scale = 0.75, roundnode/.style={thick, draw = black, fill = white, outer sep = 1.5pt, circle, minimum size = 15pt, inner sep = 1pt}]
    
    \begin{scope}[every node/.style = {roundnode = black}]
        \node (1) at (72:2) {$v_1$};
        \node (2) at (144:2) {$v_2$};
        \node (3) at (216:2) {$v_3$};
        \node (4) at (288:2) {$v_4$};
        \node (5) at (360:2) {$v_5$};
        \node[dashed] (6) at (0:0) {$v$};
    \end{scope}
    
    \begin{scope}[every node/.style = {roundnode = black}, xshift=2.5cm]
        \node[label={90:3}] (7) at (85:2) {};
        \node (8) at (30:2) {};
        \node (9) at (330:2) {};
        \node (10) at (275:2) {};
    \end{scope}

    \draw[thick]
    (1) edge (6)
    (2) edge (6)
    (3) edge (6)
    (4) edge (6)
    (5) edge (6)
    %(3) edge (4)
    ;

    \draw[thick, dashed]
    (1) edge[bend left=5] (7)
    (7) edge[bend left=10] (8)
    (8) edge[bend left=10] (9)
    (9) edge[bend left=10] (10)
    (10) edge[bend left=5] (4)
    ;
    \end{tikzpicture}

\end{document}