Question

Let A be an adjacency matrix of a graph G. The
th
ij entry in the matrix
K
A, gives
(A)
The number of paths of length K from vertex Vi to vertex Vj.
(B)
Shortest path of K edges from vertex Vi to vertex Vj.
(C)

Length of a Eulerian path from vertex Vi to vertex Vj.
(D)

Length of a Hamiltonian cycle from vertex Vi to vertex Vj

Answer 1

Answer:

           (C)Shortest path of K edges from vertex Vi to vertex Vj.

Explanation:

            An adjacency matrix is defined as follows: Let G be a graph with "$n$" vertices that are assumed to be ordered from $v_{1}$ to $v_{n}$.

The n x n matrix A, in which

           aij = 1 if there exists a path from $v_{i}$ to $v_{j}$

           aij = 0

otherwise is called an adjacency matrix.

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