GATE 2019: Network Theory Quiz 1

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Question 1

Consider the following statements for a network graph, if is its fundamental tie set matrix and and are its sub matrices corresponding to links and twigs respectively
1) is a unit matrix
2) is a rectangular matrix
3) rank of is (b-n-1)
4)
Where b is the number of branches, n is the number nodes and Q is the fundamental tie set matrix.
Which of the above statements are correct?

• A1 and 2 only
• B3 and 4 only
• C1, 2 and 4 only
• D4 only

Question 2

The number of twigs (T) & chords (L) for the given circuit respectively are: 

• AT =3 & L =3
• BT =3 & L =2
• CT =2 & L =3
• DT =4 & L =2

Question 3

The reduced incidence A_r matrix of a connected graph is given below

The following statements are associated with the above matrix:
1) Branches 1 and 6 are in parallel.
2) Branches 2 and 3 are in series.
3) Voltages of branches 1, 2, 4 and 5 form an independent set.
Which of the following statements given below is/are correct?

• A1 only
• B2 only
• C1 & 3 only
• D1 2 & 3

Question 4

A connected network of N > 2 nodes has at most one branch directly connecting any pair of nodes. The graph of the network

• Amust have at least N branches for one or more closed paths to exist
• Bcan have an unlimited number of branches
• Ccan only have at most N branches
• Dcan have a minimum number of branches not decided by N

Question 5

Which among the following network is not a traversable network?

• A
• B
• C
• D

Question 6

In a connected graph, the total number of branches is b and the total number of nodes is n. Then the number of links L of a co-tree is

• Ab - n
• Bb -n - 1
• Cb + n - 1
• Db - n + 1

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