Disproving existence of Moore Graph (v = 3250, k = 57, λ = 0, μ = 1)

In this paper, i have disproved the existence of Disproving existence of Moore Graph (v = 3250, k = 57, λ = 0, μ = 1) using the method of contradiction. I assumed this graph exists, since the graph is regular i picked a random vertex and used the definition of this Moore graph to show that there are a few constraints which dictates how the edges are defined among themselves. Eventually, using pigeonhole principle, i showed there exists at least one vertex which is common to two distinct pairs of points and based on where this common vertex is located, i derived a contradiction, thus proving that such a graph doesn't exist.