Question

Find the number of edges if the graph G has 5 vertices ,2 of degree 3 and 3 of degree 2.​

Answer 1

Answer:

We know for any graph G, the sum of the degrees of its vertices is twice its number of edges.

In this case, the sum of degrees is: 2(3)+3(2)=6+6=12

According to our fact, 12=2 times number of edges.

Therefore, number of edges=12/2= 6.

Answer 2

Concept:

In a polygon, an edge is a specific kind of line segment that connects two vertices.

The intersection of two or more curves, lines, or edges is known as a vertex.

Given:

A graph G has 5 vertices, 2 degree of 3 and 3 degree of 2.

Find:

The number of edges.

Solution:

We know that an edge connects two vertices.

Now, since each edge has been counted from both ends, the sum of the vertex degree values equals twice the number of edges.

So, the sum of degrees is:

$=2\times3+3\times2\\=12$

The sum of degrees is twice the number of edges.

Let the number of edges be $x$.

Therefore,

$2x=12\\x=\frac{12}{2}\\ x=6$

The number of edges in graph G is $6$.

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