A graph has 6 vertices, and each vertex has a degree of 2 except for one vertex, which has a degree of 4. Determine the number of edges in the graph
Question
A graph has 6 vertices, and each vertex has a degree of 2 except for one vertex, which has a degree of 4. Determine the number of edges in the graph.
Solution
To determine the number of edges in the graph, we can use the Handshaking Theorem, which states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges.
In this graph, we have 5 vertices with a degree of 2 and 1 vertex with a degree of 4.
So, the sum of the degrees of all vertices is (5*2) + 4 = 14.
According to the Handshaking Theorem, the number of edges is half of this sum.
Therefore, the number of edges in the graph is 14 / 2 = 7.
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