Are they homeomorphic? [duplicate]

general-topology

How can I determine if this two figures are homeomorphic? I'm guessing they're not homeomorphic.

I have tried using cut points but from what I understand both figures have the same number of cut points.

I can see that in the first picture the circle in the center is connected to the four other circles while in the second image every circle is connected at most to two other circles. Would this help to prove that they're not homeomorphic?

Star of circles

Line of cirlces


Solution 1:

Consider any pair of cut-points in figure one. You'll always get 4 connected sections.

For figure two consider the cut-points marked as $I$ and $E$, you'll get 3 connected sections.

The figures are not homeomorphic.

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