Even-even gracefulness of some families of graphs
IOSR Journal of Mathematics · 2013
In this paper, we prove that the Dumbbell graph, Star graph, Cartesian product n C P 2 and K 1 + C n are even-even graceful.The even-even graceful labeling of a graph G with q edges means that there is an injection f: E (G) → {2, 4,…, 2q} so that induced map f * : V (G) →{0, 2,…,(2k-2)} defined by f *(x) ≡ Σf(x, y) (mod 2k) where k = max {p, q} makes all distinct and even.