Answer
To determine if a graph is traversable or not, we need to check the number of even and odd vertices in the graph. If the number of odd vertices in a graph is more than two, the graph is not traversable.
Work Step by Step
According to the graph theory proposed by Swiss mathematician Euler, a graph can only be traversed if we can continuously trace it and do not overlap any edge, that is, each edge is traced only once. He also proved the following rules of traversability:
1. If all the vertices of the graph are even, it can be traversed. For traversing such a graph, one should start with any vertex and end at the point of beginning.
2. If there are two odd vertices in a graph, it can be traversed. One should start tracing at any of the odd vertices and finish at the other odd vertex of the graph.
3. A graph that has more than two odd vertices is not traversable.
