Which of the following statements regarding tree are correct?

(A) All the links of a tree together does not constitute the complement of the corresponding tree

(B) A connected subgraph of a connected graph is a tree if there exist (n - 1) nodes of the group

(C) A connected subgraph of a connected graph is a tree if there exist many paths between any pair of nodes in it

(D) The number of terminal nodes of end vertices of every tree are atleast two

(E) Every connected graph has atleast one tree

Choose the correct answer from the options given below:

(1) (A) and (B) only

(2) (B) and (C) only

(3) (B) and (D) only

(4) (D) and (E) only

This question was previously asked in

UGC NET Paper 2: Electronic Science Nov 2020 Official Paper

Option 4 : 4

Official Paper 1: Held on 24 Sep 2020 Shift 1

12883

50 Questions
100 Marks
60 Mins

__Properties of a tree:__

1) In a tree there exist only one and one path between any pair of nodes.

2) Every connected graph has at least one tree.

3) Every tree has at least two terminal nodes.

4) Every tree has (n – 1) branches, (n – no. of nodes)

5) The rank of a tree is (n – 1)

6) A tree contains all the nodes of the graph.

7) A tree does not contain a closed path or loop.

__Explanation:__

A tree contains all the nodes of the graph.

**Option 2 wrong.**

**∴**** Option (1) and option (2) cancel out.**

Now, Every connected graph has at least one tree.

**Option (E) correct.**

So, the only option left is Option (4) i.e. **(D) and (E) only.**

__Extra points:__

1) Number of tree branches = n – 1 (n is no. of nodes)

Twig = n – 1

= Rank of Graph

= No. of Fundamental cut-set.

2) Number of link/chords (l) = b – n + 1

= Number of KVL equation.

= Number of tie set