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1
GATE CSE 2022
MCQ (Single Correct Answer)
+1
-0.33

Consider a simple undirected unweighted graph with at least three vertices. If A is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trace of

A
A3
B
A3 divided by 2
C
A3 divided by 3
D
A3 divided by 6
2
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the minimum spanning trees of G is/are TRUE?

A
The edge with the second smallest weight is always part of any minimum spanning tree of G.
B
One or both of the edges with the third smallest and the fourth smallest weights are part of any minimum spanning tree of G.
C
Suppose S $$\subseteq$$ V be such that S $$\ne$$ $$\phi$$ and S $$\ne$$ V. Consider the edge with the minimum weight such that one of its vertices is in S and the other in V \ S. Such an edge will always be part of any minimum spanning tree of G.
D
G can have multiple minimum spanning trees.
3
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.)
4
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.
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GATE CSE Subjects
Discrete Mathematics
Graph Theory Set Theory & Algebra Combinatorics Mathematical Logic Probability Linear Algebra Calculus
Programming Languages
Basic of Programming Language Function and Recursion Pointer and Structure in C
Theory of Computation
Undecidability Finite Automata and Regular Language Push Down Automata and Context Free Language Recursively Enumerable Language and Turing Machine
Operating Systems
Process Concepts and Cpu Scheduling Synchronization and Concurrency Deadlocks Memory Management File System IO and Protection
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K Maps Boolean Algebra Combinational Circuits Number Systems Sequential Circuits
Computer Organization
Computer Arithmetic Memory Interfacing Machine Instructions and Addressing Modes IO Interface Pipelining Alu Data Path and Control Unit Secondary Memory
Database Management System
Er Diagrams Functional Dependencies and Normalization Structured Query Language Relational Algebra Transactions and Concurrency File Structures and Indexing
Data Structures
Trees Hashing Arrays Linked List Graphs Stacks and Queues
Computer Networks
Concepts of Layering Lan Technologies and Wi-Fi Data Link Layer and Switching Network Layer Routing Algorithm TCP UDP Sockets and Congestion Control Application Layer Protocol Network Security
Algorithms
Complexity Analysis and Asymptotic Notations Searching and Sorting Divide and Conquer Method Greedy Method P and NP Concepts Dynamic Programming
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