Resumen de Vertex graceful labeling of some classes of graphs.
A. P. Santhakumaran, P. Balaganesan
A connected graph G = (V, E) of order atleast two, with order p and size q is called vertex-graceful if there exists a bijection f : V → {1, 2, 3, ··· p} such that the induced function f ∗ : E → {0, 1, 2, ··· q − 1} defined by f ∗ (uv) = (f(u) + f(v))(mod q) is a bijection. The bijection f is called a vertex-graceful labeling of G. A subset S of the set of natural numbers N is called consecutive if S consists of consecutive integers. For any set X, a mapping f : X → N is said to be consecutive if f(X) is consecutive. A vertex-graceful labeling f is said to be strong if the function f1 : E → N defined by f1(e) = f(u)+ f(v) for all edges e = uv in E forms a consecutive set. It is proved that one vertex union of odd number of copies of isomorphic caterpillars is vertex-graceful and any caterpillar is strong vertex-graceful. It is proved that a spider with even number of legs (paths) of equal length appended to each vertex of an odd cycle is vertex-graceful. It is also proved that the graph lA(mj , n) is vertex-graceful for both n and l odd, 0 ≤ i ≤ n − 1, 1 ≤ j ≤ mi. Further, it is proved that the graph A(mj , n) is strong vertex-graceful for n odd, 0 ≤ i ≤ n − 1, 1 ≤ j ≤ mi.
