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According to network graphs, the network with: 1. Only two odd vertices is traversable 2. No odd vertices is traversable 3. Two or more than two odd vertices are traversable Which of the above statements is / are correct?

According to network graphs, the network with: 1. Only two odd vertices is traversable 2. No odd vertices is traversable 3. Two or more than two odd vertices are traversable Which of the above statements is / are correct? Correct Answer 1 and 2

Vertex (Vertices): Each point of a graph

Edge: An edge is a segment that connects two vertices.

A network is said to traversable if it can be traced in one sweep without lifting the pencil from the paper and without tracing the same edge more than once.

The degree of a vertex is the number of edges that meet at that vertex. If the degree of a vertex is odd then it is odd vertex, otherwise it is even vertex.

Conditions to be traversable:

  • If the network has no odd vertices, then the network is traversable, and any point is a starting point. The starting point will also turn out to be the ending point.
  • If the network has exactly one odd vertex, then the network is not traversable. A network cannot have only one starting point or ending point without the other.
  • If the network has two odd vertices, then the network is traversable. One odd vertex must be the starting point and the other odd vertex must be the ending point.
  • If the network has more than two odd vertices, then the network is not traversable. A network cannot have more than one starting point and one ending point.

 

Example:

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Network 1 is traversable since the graph has two odd vertices and four even vertices. Vertices A and F are odd and vertices B, C, D, and E are even.

Network 2 is not traversable because it has four odd vertices which are A, B, C, and D.

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