Virtual Gate Test Series: Discrete Mathematics - Graph Theory

Question

Consider the following two statements$:$

1. The two graphs $G_{1}$ and $G_{2}$ are isomorphic
2. Each of $G_{1}$ and $G_{2}$ are self-dual.

 

1. Both $(i)$ and $(ii)$ are true
2. Only $(i)$ is true
3. Only $(ii)$ is true
4. Both $(i)$ and $(ii)$ are false

Answer 1

Stretching the vertex in the center of $G_1$ to the top makes it $G_2$, Hence both are Isomorphic to each other.

A plane graph is said to be self-dual if it is isomorphic to its dual graph.

$G_1$ is self dual, Infact all wheel graphs are self dual

$G_2$ is self dual too, $G_2$ is isomorphic to $G_1$ so first we need to convert it to planer graph which is $G_1$ then dual of it will be isomorphic as shown in figure above hence both $(i)$ and $(ii)$ are true.

 

Comments

@utkarsh i only knows about isomorphism

I didn't understood this A plane graph is said to be self-dual if it is isomorphic to its dual graph.

Can you explain it a bit more with any example

Thnxx :)

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Prince watch this https://youtu.be/grh0Dnpr4JI

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@utkarsh thnxx :)

The video cleared my doubt