Question

suppose a simple graph has 10 edges 5 vertices of degree 6,4 vertices of degree 3 and all others of 2. how many vertices does the graph have?​

Answer 1

Answer:

These are very straightforward questions. If you had taken the trouble of opening your textbook, you would not be asking this question. You must make an effort to try problems yourself first. You gain very little having your questions answered without first trying.

The first theorem of Graph Theory says that the sum of all vertex degrees equals twice the number of edges. So if there are  n  vertices in the graph, then  (3⋅4)+2(n−3)=2⋅9=18 . This gives  n=6

Step-by-step explanation:

Answer 2

Given,

A simple graph has $\[10\]$ edges $\[5\]$ vertices of degree$\[6\]$,$\[4\]$ vertices of degree $\[3\]$ and all others of $\[2\]$ .

Solution,

Know that according to graph theory, the sum of all vertex degrees equals twice the number of edges.

Assume that the vertices are $\[n.\]$

Therefore,

$\[\begin{array}{l} \Rightarrow \left( {3 \times 4} \right) + 2\left( {n - 3} \right) = 2 \times 9\\ \Rightarrow 12 + 2n - 6 = 18\\ \Rightarrow 2n + 6 = 18\\ \Rightarrow 2n = 18 - 6\\ \Rightarrow 2n = 12\\ \Rightarrow n = 6\end{array}\]$

Hence, the number of vertices is $\[6.\]$