For which of the following graphs Euler circuit does not exist?

C o m p l e t e b i p a r t i t e g r a p h K_{4, 2}

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C o m p l e t e g r a p h K_{9}

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C y c l e g r a p h C_{9}

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W h e e l g r a p h W_{6}

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Solution

The correct option is D $W h e e l g r a p h W_{6}$
In a connected graph, Euler circuit exist iff all the vertices in the graph are of even degree.
In a wheel graph $W_{6}$ , we have 5 vertices with degree 3 and 1 vertex degree 5.
Therefore, Euler circuit does not exist in $W_{6}$ .

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