Let A be the adjacency matrix of the graph with vertices {1, 2, 3, 4, 5}.
Let λ1, λ2, λ3, λ4, and λ5 be the five eigenvalues of A. Note that these eigenvalues need not be distinct.
The value of λ1 + λ2 + λ3 + λ4 + λ5 = ______.
Correct Answer:
2
Solution:
Adjacency Matrix of A =
The sum of eigenvalues of A = trace of A
= λ1 + λ2 + λ3 + λ4 + λ5
= 0 + 0 + 1 + 1 + 0 = 2