Exams › GATE › Technical

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

1. A³
2. A³ divided by 2
3. A³ divided by 3
4. A³ divided by 6

Correct answer: A³ divided by 6

Solution

The number of 3-cycles in an undirected graph can be found by calculating the trace of the cube of the adjacency matrix, A³, which counts each cycle three times (once for each vertex in the cycle). Therefore, to get the correct count of unique 3-cycles, we divide the trace of A³ by 6, accounting for the overcounting.

Related GATE Technical questions

• Which one of the following regular expressions correctly represents the language of the finite automaton given below?
• Which one of the following statements is TRUE?
• In a relational data model, which one of the following statements is TRUE?
• Consider the problem of reversing a singly linked list. To take an example, given the linked list below, head -> a -> b -> c -> d -> e -> NULL, the reversed linked list should look like head -> e -> d -> c -> b -> a -> NULL. Which one of the following statements is TRUE about the time complexity of algorithms that solve the above problem in O(1) space?
• Suppose we are given n keys, m hash table slots, and two simple uniform hash functions h1 and h2. Further suppose our hashing scheme uses h1 for the odd keys and h2 for the even keys. What is the expected number of keys in a slot?
• Which one of the following facilitates transfer of bulk data from hard disk to main memory with the highest throughput?

⚔️ Practice GATE Technical free + battle 1v1 →