Negative Peble Graph is one with \(n\) vertices \(\left\{ {v_{1} ,v_{2} , \cdots , v_{n} } \right\} \) and the adjacency between the vertices is carried out by the condition based on divisibility. Here the vertices \(v^{\prime}_{i} s\) are ordered pairs \(\left( {x_{i} ,y_{i} } \right)\) where \(x_{i}^{2} - dy_{i}^{2} = - 1\) for some particular choices of \(d\) . This paper focuses on such types of graphs and aims to study their behavior.