Edge even graceful labeling of [formula omitted] and [formula omitted

Abstract

For a graph G(V,E), with EG=m and VG=n, the edge even graceful labeling is a bijection f:EG→{2,4,6,⋯,2m} such that, each vertex vi is assigned by the color ∑fvivjmod2r. Where r=max{n,m},vj∈Nvi,vivj∈EG, the resulting vertex label is distinct. In this article the graphs TPn, a rooted tree T with root vertex of degree d-1 and internal vertices of odd degree d, Frn3 and Fn=K1+Pn, Wn proved as an edge even graceful graph.