On an Algorithm for Ordering of Graphs

Let (G, ρ) be a finite connected (undirected) graph without loops and multiple edges. So x, y being two elements of G (vertices of the graph (G, ρ)), 〈x, y〉 ∊ ρ means that x and y are connected by an edge. Two vertices x, y ∊ G have the distance μ(x, y) equal to n, if n is the smallest number with the following property: there exists a sequence x 0, x 1, …, xn of vertices such that x 0 = x, xn = y and 〈x i-1, Xi 〉 ∊ ρ for i = 1, …, n. If x ∊ G, we put μ(x, x) = 0.