File:Nonisomorphic medial graph example.svg
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Summary
| Description |
English: Two embeddings of the same graph (in blue) can have nonisomorphic medial graphs (in red). |
| Date | |
| Source |
\documentclass{article}
\thispagestyle{empty}
\usepackage[margin=0in]{geometry}
\usepackage{tikz}
\def\nodeDist{2.5cm}
\tikzstyle{origVertex} = [draw, blue, fill, shape=circle]
\tikzstyle{newVertex} = [draw, red, fill, shape=circle]
\tikzstyle{invisibleVertex} = [shape=circle]
\tikzstyle{origEdge} = [blue]
\tikzstyle{newEdge} = [red, densely dashed]
\tikzstyle{invisibleEdge} = [draw opacity=0]
\begin{document}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
\node[origVertex] (0) {};
\node[origVertex] (1) [below of=0] {};
\node[origVertex] (2) [left of=1] {};
\node[origVertex] (3) [right of=1] {};
\node[origVertex] (4) [below of=1] {};
\node[origVertex] (5) [below of=4] {};
\path (0) edge[origEdge] node[invisibleVertex] (m0) {} (2)
edge[origEdge] node[invisibleVertex] (m1) {} (3)
(1) edge[origEdge] node[invisibleVertex] (m2) {} (4)
(2) edge[origEdge] node[invisibleVertex] (m3) {} (4)
(3) edge[origEdge] node[invisibleVertex] (m4) {} (4)
(4) edge[origEdge] node[invisibleVertex] (m5) {} (5);
\path (m0) edge[invisibleEdge, out= 90, in= 90, looseness=2] (m1)
edge[invisibleEdge] (m1)
edge[invisibleEdge, out= 180, in= 180, looseness=2] (m3)
edge[invisibleEdge] (m3)
(m1) edge[invisibleEdge, out= 0, in= 0, looseness=2] (m4)
edge[invisibleEdge] (m4)
(m2) edge[invisibleEdge, out= 125, in= 55, looseness=30] (m2)
edge[invisibleEdge] (m3)
edge[invisibleEdge] (m4)
(m3) edge[invisibleEdge, bend right] (m5)
(m4) edge[invisibleEdge, bend left] (m5)
(m5) edge[invisibleEdge, out=-125, in= -55, looseness=30] (m5);
\end{tikzpicture}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
\node[origVertex] (0) {};
\node[origVertex] (1) [below of=0] {};
\node[origVertex] (2) [left of=1] {};
\node[origVertex] (3) [right of=1] {};
\node[origVertex] (4) [below of=1] {};
\node[origVertex] (5) [below of=4] {};
\path (0) edge[origEdge] node[newVertex] (m0) {} (2)
edge[origEdge] node[newVertex] (m1) {} (3)
(1) edge[origEdge] node[newVertex] (m2) {} (4)
(2) edge[origEdge] node[newVertex] (m3) {} (4)
(3) edge[origEdge] node[newVertex] (m4) {} (4)
(4) edge[origEdge] node[newVertex] (m5) {} (5);
\path (m0) edge[newEdge, out= 90, in= 90, looseness=2] (m1)
edge[newEdge] (m1)
edge[newEdge, out= 180, in= 180, looseness=2] (m3)
edge[newEdge] (m3)
(m1) edge[newEdge, out= 0, in= 0, looseness=2] (m4)
edge[newEdge] (m4)
(m2) edge[newEdge, out= 125, in= 55, looseness=30] (m2)
edge[newEdge] (m3)
edge[newEdge] (m4)
(m3) edge[newEdge, bend right] (m5)
(m4) edge[newEdge, bend left] (m5)
(m5) edge[newEdge, out=-125, in= -55, looseness=30] (m5);
\end{tikzpicture}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
\node[invisibleVertex] (0) {};
\node[invisibleVertex] (1) [below of=0] {};
\node[invisibleVertex] (2) [left of=1] {};
\node[invisibleVertex] (3) [right of=1] {};
\node[invisibleVertex] (4) [below of=1] {};
\node[invisibleVertex] (5) [below of=4] {};
\path (0) edge[invisibleEdge] node[newVertex] (m0) {} (2)
edge[invisibleEdge] node[newVertex] (m1) {} (3)
(1) edge[invisibleEdge] node[newVertex] (m2) {} (4)
(2) edge[invisibleEdge] node[newVertex] (m3) {} (4)
(3) edge[invisibleEdge] node[newVertex] (m4) {} (4)
(4) edge[invisibleEdge] node[newVertex] (m5) {} (5);
\path (m0) edge[newEdge, out= 90, in= 90, looseness=2] (m1)
edge[newEdge] (m1)
edge[newEdge, out= 180, in= 180, looseness=2] (m3)
edge[newEdge] (m3)
(m1) edge[newEdge, out= 0, in= 0, looseness=2] (m4)
edge[newEdge] (m4)
(m2) edge[newEdge, out= 125, in= 55, looseness=30] (m2)
edge[newEdge] (m3)
edge[newEdge] (m4)
(m3) edge[newEdge, bend right] (m5)
(m4) edge[newEdge, bend left] (m5)
(m5) edge[newEdge, out=-125, in= -55, looseness=30] (m5);
\end{tikzpicture}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
\node[origVertex] (0) {};
\node[invisibleVertex] (1) [below of=0] {};
\node[origVertex] (2) [left of=1] {};
\node[origVertex] (3) [right of=1] {};
\node[origVertex] (4) [below of=1] {};
\node[origVertex] (5) [below left of=4] {};
\node[origVertex] (6) [below right of=4] {};
\path (0) edge[origEdge] node[invisibleVertex] (m0) {} (2)
edge[origEdge] node[invisibleVertex] (m1) {} (3)
(2) edge[origEdge] node[invisibleVertex] (m2) {} (4)
(3) edge[origEdge] node[invisibleVertex] (m3) {} (4)
(4) edge[origEdge] node[invisibleVertex] (m4) {} (5)
edge[origEdge] node[invisibleVertex] (m5) {} (6);
\path (m0) edge[invisibleEdge, out= 90, in= 90, looseness=2] (m1)
edge[invisibleEdge] (m1)
edge[invisibleEdge, out= 180, in= 180, looseness=2] (m2)
edge[invisibleEdge] (m2)
(m1) edge[invisibleEdge, out= 0, in= 0, looseness=2] (m3)
edge[invisibleEdge] (m3)
(m2) edge[invisibleEdge] (m3)
edge[invisibleEdge] (m4)
(m3) edge[invisibleEdge] (m5)
(m4) edge[invisibleEdge, out=-170, in=-100, looseness=30] (m4)
edge[invisibleEdge] (m5)
(m5) edge[invisibleEdge, out= -80, in= -10, looseness=30] (m5);
\end{tikzpicture}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
\node[origVertex] (0) {};
\node[invisibleVertex] (1) [below of=0] {};
\node[origVertex] (2) [left of=1] {};
\node[origVertex] (3) [right of=1] {};
\node[origVertex] (4) [below of=1] {};
\node[origVertex] (5) [below left of=4] {};
\node[origVertex] (6) [below right of=4] {};
\path (0) edge[origEdge] node[newVertex] (m0) {} (2)
edge[origEdge] node[newVertex] (m1) {} (3)
(2) edge[origEdge] node[newVertex] (m2) {} (4)
(3) edge[origEdge] node[newVertex] (m3) {} (4)
(4) edge[origEdge] node[newVertex] (m4) {} (5)
edge[origEdge] node[newVertex] (m5) {} (6);
\path (m0) edge[newEdge, out= 90, in= 90, looseness=2] (m1)
edge[newEdge] (m1)
edge[newEdge, out= 180, in= 180, looseness=2] (m2)
edge[newEdge] (m2)
(m1) edge[newEdge, out= 0, in= 0, looseness=2] (m3)
edge[newEdge] (m3)
(m2) edge[newEdge] (m3)
edge[newEdge] (m4)
(m3) edge[newEdge] (m5)
(m4) edge[newEdge, out=-170, in=-100, looseness=30] (m4)
edge[newEdge] (m5)
(m5) edge[newEdge, out= -80, in= -10, looseness=30] (m5);
\end{tikzpicture}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
\node[invisibleVertex] (0) {};
\node[invisibleVertex] (1) [below of=0] {};
\node[invisibleVertex] (2) [left of=1] {};
\node[invisibleVertex] (3) [right of=1] {};
\node[invisibleVertex] (4) [below of=1] {};
\node[invisibleVertex] (5) [below left of=4] {};
\node[invisibleVertex] (6) [below right of=4] {};
\path (0) edge[invisibleEdge] node[newVertex] (m0) {} (2)
edge[invisibleEdge] node[newVertex] (m1) {} (3)
(2) edge[invisibleEdge] node[newVertex] (m2) {} (4)
(3) edge[invisibleEdge] node[newVertex] (m3) {} (4)
(4) edge[invisibleEdge] node[newVertex] (m4) {} (5)
edge[invisibleEdge] node[newVertex] (m5) {} (6);
\path (m0) edge[newEdge, out= 90, in= 90, looseness=2] (m1)
edge[newEdge] (m1)
edge[newEdge, out= 180, in= 180, looseness=2] (m2)
edge[newEdge] (m2)
(m1) edge[newEdge, out= 0, in= 0, looseness=2] (m3)
edge[newEdge] (m3)
(m2) edge[newEdge] (m3)
edge[newEdge] (m4)
(m3) edge[newEdge] (m5)
(m4) edge[newEdge, out=-170, in=-100, looseness=30] (m4)
edge[newEdge] (m5)
(m5) edge[newEdge, out= -80, in= -10, looseness=30] (m5);
\end{tikzpicture}
\end{document}
|
| Author | Self |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:20, 9 December 2012 | | 699 × 598 (55 KB) | Bender2k14 | {{Information |Description ={{en|1=Two embeddings of the same graph (in blue) can have nonisomorphic medial graphs (in red).}} |Source =<source lang="latex"> \documentclass{article} \thispagestyle{empty} \usepackage[margin=0in]{geometry} \us... |
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