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| Keywords: Nonisomorphic medial graph example.svg en Two embeddings of the same graph in blue can have nonisomorphic medial graphs in red <source lang latex > \documentclass article \thispagestyle empty \usepackagemargin 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 \nodeorigVertex 0 ; \nodeorigVertex 1 below of 0 ; \nodeorigVertex 2 left of 1 ; \nodeorigVertex 3 right of 1 ; \nodeorigVertex 4 below of 1 ; \nodeorigVertex 5 below of 4 ; \path 0 edgeorigEdge nodeinvisibleVertex m0 2 edgeorigEdge nodeinvisibleVertex m1 3 1 edgeorigEdge nodeinvisibleVertex m2 4 2 edgeorigEdge nodeinvisibleVertex m3 4 3 edgeorigEdge nodeinvisibleVertex m4 4 4 edgeorigEdge nodeinvisibleVertex m5 5 ; \path m0 edgeinvisibleEdge out 90 in 90 looseness 2 m1 edgeinvisibleEdge m1 edgeinvisibleEdge out 180 in 180 looseness 2 m3 edgeinvisibleEdge m3 m1 edgeinvisibleEdge out 0 in 0 looseness 2 m4 edgeinvisibleEdge m4 m2 edgeinvisibleEdge out 125 in 55 looseness 30 m2 edgeinvisibleEdge m3 edgeinvisibleEdge m4 m3 edgeinvisibleEdge bend right m5 m4 edgeinvisibleEdge bend left m5 m5 edgeinvisibleEdge out -125 in -55 looseness 30 m5 ; \end tikzpicture \begin tikzpicture node distance \nodeDist semithick \nodeorigVertex 0 ; \nodeorigVertex 1 below of 0 ; \nodeorigVertex 2 left of 1 ; \nodeorigVertex 3 right of 1 ; \nodeorigVertex 4 below of 1 ; \nodeorigVertex 5 below of 4 ; \path 0 edgeorigEdge nodenewVertex m0 2 edgeorigEdge nodenewVertex m1 3 1 edgeorigEdge nodenewVertex m2 4 2 edgeorigEdge nodenewVertex m3 4 3 edgeorigEdge nodenewVertex m4 4 4 edgeorigEdge nodenewVertex m5 5 ; \path m0 edgenewEdge out 90 in 90 looseness 2 m1 edgenewEdge m1 edgenewEdge out 180 in 180 looseness 2 m3 edgenewEdge m3 m1 edgenewEdge out 0 in 0 looseness 2 m4 edgenewEdge m4 m2 edgenewEdge out 125 in 55 looseness 30 m2 edgenewEdge m3 edgenewEdge m4 m3 edgenewEdge bend right m5 m4 edgenewEdge bend left m5 m5 edgenewEdge out -125 in -55 looseness 30 m5 ; \end tikzpicture \begin tikzpicture node distance \nodeDist semithick \nodeinvisibleVertex 0 ; \nodeinvisibleVertex 1 below of 0 ; \nodeinvisibleVertex 2 left of 1 ; \nodeinvisibleVertex 3 right of 1 ; \nodeinvisibleVertex 4 below of 1 ; \nodeinvisibleVertex 5 below of 4 ; \path 0 edgeinvisibleEdge nodenewVertex m0 2 edgeinvisibleEdge nodenewVertex m1 3 1 edgeinvisibleEdge nodenewVertex m2 4 2 edgeinvisibleEdge nodenewVertex m3 4 3 edgeinvisibleEdge nodenewVertex m4 4 4 edgeinvisibleEdge nodenewVertex m5 5 ; \path m0 edgenewEdge out 90 in 90 looseness 2 m1 edgenewEdge m1 edgenewEdge out 180 in 180 looseness 2 m3 edgenewEdge m3 m1 edgenewEdge out 0 in 0 looseness 2 m4 edgenewEdge m4 m2 edgenewEdge out 125 in 55 looseness 30 m2 edgenewEdge m3 edgenewEdge m4 m3 edgenewEdge bend right m5 m4 edgenewEdge bend left m5 m5 edgenewEdge out -125 in -55 looseness 30 m5 ; \end tikzpicture \begin tikzpicture node distance \nodeDist semithick \nodeorigVertex 0 ; \nodeinvisibleVertex 1 below of 0 ; \nodeorigVertex 2 left of 1 ; \nodeorigVertex 3 right of 1 ; \nodeorigVertex 4 below of 1 ; \nodeorigVertex 5 below left of 4 ; \nodeorigVertex 6 below right of 4 ; \path 0 edgeorigEdge nodeinvisibleVertex m0 2 edgeorigEdge nodeinvisibleVertex m1 3 2 edgeorigEdge nodeinvisibleVertex m2 4 3 edgeorigEdge nodeinvisibleVertex m3 4 4 edgeorigEdge nodeinvisibleVertex m4 5 edgeorigEdge nodeinvisibleVertex m5 6 ; \path m0 edgeinvisibleEdge out 90 in 90 looseness 2 m1 edgeinvisibleEdge m1 edgeinvisibleEdge out 180 in 180 looseness 2 m2 edgeinvisibleEdge m2 m1 edgeinvisibleEdge out 0 in 0 looseness 2 m3 edgeinvisibleEdge m3 m2 edgeinvisibleEdge m3 edgeinvisibleEdge m4 m3 edgeinvisibleEdge m5 m4 edgeinvisibleEdge out -170 in -100 looseness 30 m4 edgeinvisibleEdge m5 m5 edgeinvisibleEdge out -80 in -10 looseness 30 m5 ; \end tikzpicture \begin tikzpicture node distance \nodeDist semithick \nodeorigVertex 0 ; \nodeinvisibleVertex 1 below of 0 ; \nodeorigVertex 2 left of 1 ; \nodeorigVertex 3 right of 1 ; \nodeorigVertex 4 below of 1 ; \nodeorigVertex 5 below left of 4 ; \nodeorigVertex 6 below right of 4 ; \path 0 edgeorigEdge nodenewVertex m0 2 edgeorigEdge nodenewVertex m1 3 2 edgeorigEdge nodenewVertex m2 4 3 edgeorigEdge nodenewVertex m3 4 4 edgeorigEdge nodenewVertex m4 5 edgeorigEdge nodenewVertex m5 6 ; \path m0 edgenewEdge out 90 in 90 looseness 2 m1 edgenewEdge m1 edgenewEdge out 180 in 180 looseness 2 m2 edgenewEdge m2 m1 edgenewEdge out 0 in 0 looseness 2 m3 edgenewEdge m3 m2 edgenewEdge m3 edgenewEdge m4 m3 edgenewEdge m5 m4 edgenewEdge out -170 in -100 looseness 30 m4 edgenewEdge m5 m5 edgenewEdge out -80 in -10 looseness 30 m5 ; \end tikzpicture \begin tikzpicture node distance \nodeDist semithick \nodeinvisibleVertex 0 ; \nodeinvisibleVertex 1 below of 0 ; \nodeinvisibleVertex 2 left of 1 ; \nodeinvisibleVertex 3 right of 1 ; \nodeinvisibleVertex 4 below of 1 ; \nodeinvisibleVertex 5 below left of 4 ; \nodeinvisibleVertex 6 below right of 4 ; \path 0 edgeinvisibleEdge nodenewVertex m0 2 edgeinvisibleEdge nodenewVertex m1 3 2 edgeinvisibleEdge nodenewVertex m2 4 3 edgeinvisibleEdge nodenewVertex m3 4 4 edgeinvisibleEdge nodenewVertex m4 5 edgeinvisibleEdge nodenewVertex m5 6 ; \path m0 edgenewEdge out 90 in 90 looseness 2 m1 edgenewEdge m1 edgenewEdge out 180 in 180 looseness 2 m2 edgenewEdge m2 m1 edgenewEdge out 0 in 0 looseness 2 m3 edgenewEdge m3 m2 edgenewEdge m3 edgenewEdge m4 m3 edgenewEdge m5 m4 edgenewEdge out -170 in -100 looseness 30 m4 edgenewEdge m5 m5 edgenewEdge out -80 in -10 looseness 30 m5 ; \end tikzpicture \end document </source> Self 2012-12-09 Undirected planar graphs Images with LaTeX source code Cc-zero | ||||
