For each of the following 3 graphs either draw it without an

For each of the following 3 graphs, either draw it without any edge crossings, or explain how you know it\'s impossible to do so.

Solution

The problem is straightforward of finding whether a Euler Circuit exists in Graph or not. If Euler circuit exists , then figure can be drawn without any edge crossing.

A Euler Circuit is a closed path that uses every edge of a graph exactly once.

Sufficient Condition to prove Graph doesn\'t contain a Euler Circuit:

If the number of odd vertices in Graph G is anything other than 0, then G cannot have a Euler Circuit.

Clearly, A, B and C don\'t have Euler Circuit\'s because they have at least one vertex with odd degree.