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UGC NET Computer Science Nov 2021 (Paper II)

For which value of $n$ is Wheel graph $W_n$ regular?

Solution

A wheel graph $W_n$ has one central vertex connected to all vertices of a cycle.

In $W_n$, the central vertex has degree $n-1$.

Each outer vertex has degree $3$, because it is connected to two cycle vertices and one central vertex.

For the graph to be regular:

$n-1=3$

$n=4$

So, $W_4$ is regular.

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