A graph without an Euler circuit but with an Euler path

[shofmannx20]

Question 1

A graph has an Euler circuit if
◦ it is connected and has an even number of vertices.
◦ it is connected and every vertex has even degree.
◦ every vertex has even degree.
◦ it is connected and has an even number of edges.
◦ none of these

Question 2

A graph without an Euler circuit but with an Euler path
◦ must be connected and have exactly two vertices of odd degree.
◦ must be connected and have exactly one vertex of odd degree.
◦ must be connected and every vertex must have even degree.
◦ must be connected and every vertex must have odd degree.
◦ none of these

[jasonq]

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[shofmannx20]

Thanks for the timely response, appreciate it

[yeungji]

Great answer, keep it coming