Asymptotic behaviour of the observability of Qn Original Research Article

Observability of a graph G is the minimum k for which the edges of G can be properly coloured with k colours in such a way that colour sets of vertices of G (sets of colours of their incident edges) are pairwise distinct. It is shown that limn→∞ obs(Qn)n = 1 + q∗ where q∗ = 0.293815 … is the unique solution of the equation (x + 1)x+1 = 2xx in the interval (0, ∞).