Unable to show that the graph is planar

graph theoryplanar-graphs

How to show that the following graph is planar?

enter image description here

I tried to redraw the graph but I cant draw it without the edges crossing.

Also I find that the edges $3,4,5$ form a complete graph.
Also I am unable to find any subdivision of $K_5$ or $K_{3,3}$.
So I am confused whether it is planar or not?

Best Answer

Place vertices $5$ and $1$ inside triangle $234$.enter image description here Graph with $5$ vertices can't be subdivision of $K_{3,3}$, and it can be subdivision of $K_5$ only if it's $K_5$ itself.

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