Mathematics Assignment on the La Tex software

Question 1 

Solution

In the above given set of the edges first we select the edge by the least weight that is

Now from the remaining edges  is a next edge which is also selected, and thus it has minimum weight now.

After this, we will select edge  because it has the minimum out of the remaining edges.

After this we will select edge  because it has minimum out of the remaining edges.

After this we cannot select edges  ,  and  because all three edges make a cycle, so we will select the edge  which will complete the MST.

The selected edges are:

Question 2

Question 3

Solution

a) 

b) This graph is possible because the number of vertices with odd degrees must be even according to handshaking lemma

c) Total number of edges will (1+1+1+2+4+4+5)/2 = 9, so the tree is not possible because a tree with n nodes has (n – 1) edges.

d)

f) It’s not possible, because we need to draw a graph with no cycles, the graph has 5 vertices and two vertices with 4 degree which will introduce a cycle.

Question 4

Solution;

We can write the characteristic equations for this recurrence relation as:

Question 5

Solution