1
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

The following simple undirected graph is referred to as the Peterson graph.

GATE CSE 2022 Discrete Mathematics - Graph Theory Question 6 English

Which of the following statements is/are TRUE?

A
The chromatic number of the graph is 3.
B
The graph has a Hamiltonian path.
C

The following graph is isomorphic to the Peterson graph.

GATE CSE 2022 Discrete Mathematics - Graph Theory Question 6 English Option 3

D
The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)
2
GATE CSE 2022
MCQ (Single Correct Answer)
+1
-0.33

Which of the properties hold for the adjacency matrix A of a simple undirected unweighted graph having n vertices?

A
The diagonal entries of A2 are the degrees of the vertices of the graph.
B
If the graph is connected, then none of the entries of An $$-$$ 1 + In can be zero.
C
If the sum of all the elements of A is at most 2(n $$-$$ 1), then the graph must be acyclic.
D
If there is at least a 1 in each of A's rows and columns, then the graph must be connected.
3
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Which of the following is/are the eigen vector(s) for the matrix given below?

$$\left( {\matrix{ { - 9} & { - 6} & { - 2} & { - 4} \cr { - 8} & { - 6} & { - 3} & { - 1} \cr {20} & {15} & 8 & 5 \cr {32} & {21} & 7 & {12} \cr } } \right)$$

A
$$\left( {\matrix{ { - 1} \cr 1 \cr 0 \cr 1 \cr } } \right)$$
B
$$\left( {\matrix{ 1 \cr 0 \cr { - 1} \cr 0 \cr } } \right)$$
C
$$\left( {\matrix{ { - 1} \cr 0 \cr 2 \cr 2 \cr } } \right)$$
D
$$\left( {\matrix{ 0 \cr 1 \cr { - 3} \cr 0 \cr } } \right)$$
4
GATE CSE 2022
MCQ (Single Correct Answer)
+1
-0.33

Consider the following threads, T1, T2 and T3 executing on a single processor, synchronized using three binary semaphore variables, S1, S2 and S3, operated upon using standard wait( ) and signal( ). The threads can be context switched in any order and at any time.

$${T_1}$$ $${T_2}$$ $${T_3}$$
while (true) {
wait ($${S_3}$$);
print ("C");
signal ($${S_2}$$); }
while (true) {
wait ($${S_1}$$);
print ("B");
signal ($${S_3}$$); }
while (true) {
wait ($${S_2}$$);
print ("A")
signal ($${S_1}$$); }

Which initialization of the semaphores would print the sequence BCABCABCA....... ?

A
S1 = 1; S2 = 1; S3 = 1
B
S1 = 1; S2 = 1; S3 = 0
C
S1 = 1; S2 = 0; S3 = 0
D
S0 = 1; S2 = 1; S3 = 1
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