Assignment On Three Connected Components In The Subgraph

GAME THEORY
Question 1
a) {a, b, c, d, e}
There are three connected components in the subgraph as shown below:
{a , b , c , d , e }
b) {f, g, h, I, j}
There is one connected component in the subgraph induced by the vertices {f, g, h, I,
j} as shown below:
{f , g ,h , i , j}
c) {a, b, e, h, i}
There three connected components in the subgraph induced by the vertices {a, b, e, h,
i} as shown below:

{a , b , e , h ,i }
d) {c, f, g, I, j}
There are two connected components as shown below:
e) {a, c, d, g, j}
There are five connected components in the subgraph induced by the vertices {a, c, d, g,
j} as shown below:
Question 2

If G is a graph in which any two nodes or vertices are connected by a unique path then G is a
tree.
There is the existence of a path between every pair of vertices so we assume that graph G is
connected. A circuit in a graph implies that there is at least one pair of vertices a and b, such
that there are two distinct paths between a and b. Since G has one and only one path between
every pair of vertices. G cannot have any circuit. Hence graph G is a tree as shown below:
Question 3
a) With the degree sequence, {4,2,1,1,1,1) the following graph can be sketched:
In this case,
d ( V 1 )=4
d ( V 2 ) =2