On indexable graphs

Let G = (V, E) be a (p, q) graph. G is said to be strongly indexable if there exists a bijection f: V → {0, 1, 2, …, p - 1} such that f+ (E) = {1, 2, …, q}, where f+ (uv) = f(u) + f(v) for any edge uv ∈ E. G is said to be indexable if f+ is injective on E. In this paper we construct classes of strongly indexable unicyclic graphs. We also prove that trees and unicyclic graphs are indexable.