GATEverse — GATE CSE previous year questions

Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as:

\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortest path between $u$ and $v$}\}

Let $M$ be the adjacency matrix of $G$ . Define graph $G_2$ on the same set of vertices with adjacency matrix $N$ , where

N_{ij}=\left\{\begin{array} {lll} 1 &\text{if}\; M_{ij}>0 \text{ or } P_{ij}>0, \text{ where }P=M^2\\0 &\text{otherwise} \end{array}\right.

Which one of the following statements is true?