I was wondering if I were given an exercise where I have to find edge and vertex connectivity of a graph which representation is given and if its obvious from the image that edge and vertex connectivity is for example 3, do I have to prove that and what is the way to do so instead of writing every single combination?

Let this be an example :

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[![enter image description here](https://i.stack.imgur.com/rE3YB.png)](https://i.stack.imgur.com/rE3YB.png)

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It is obvious that after removing edges $b$,$c$ and $a$ graph becomes disconnected and thus the edge-connectivity is 3. So now I know that vertex connectivity has to be $\leq 3$ from $\delta(G) \ge \kappa\_e (G) \ge \kappa\_v (G)$ where $\kappa\_e(G)$ is edge-connectivity and $\kappa\_v(G)$ is vertex-connectivity. We can also see that vertex connectivity is $2$ because there is no way to remove one vertex so that graph becomes disconnected. $2$ is the minimum number of vertices needed to disconnect graph after their removal.

How do I mathematically prove this?