1: Construct a simple graph containing 4 vertices and 5 edges. List the degree o

Question

1: Construct a simple graph containing 4 vertices and 5 edges. List the degree of each vertex N 2: What is the minimum number of vertices of odd degree for any simple graph? 3: Consider a simple graph. The introduction of an edge to this simple graph can either connect two already existing vertices, or connect one new vertex to one existing vertex. For any simple graph, this has an effect on the number of vertices of odd degree. Create a brief table of all the various possibilities and use this to demonstrate that the number of vertices of odd degree in a simple graph is always an even number 4: The graph of a star contains n vertices. What is the degree of each vertex in the graph? 5: The graph of a star contains n vertices. If one vertex is labeled as vertex A, how many possible routes can be taken from vertex A to create a path which visits all n vertices WITHOUT repeating an edge?

Explanation / Answer

1. Without loop it is not possible to have 4 vertices and 5 edges.

So degree of vertices of such graph can not be defined.

Had the loop be allowed,

2 of these vertices would be of degree 3 and rest 2 would be of degree 2.

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