Edge-gracefulness of the composition of paths with null graphs Original Research Article

Let G = (V,E) be a (p,q)-graph. Let f : E→{1,2,…,q} be a bijection. The induced mapping f+ : V→Zp of f is defined by f+(u)≡∑uv∈Ef(uv) (modp) for u∈V. If f+ is a bijection, then G is called edge-graceful. In this paper, we investigate the edge-gracefulness of the composition of paths with null graphs Pm∘Nn, where there are mn vertices and (m−1)n2 edges. We show that P3∘Nn is edge-graceful if n is odd.