On the Gracefulness of the Digraph (P)over-right-arrow(a,b)

摘要

A digraph D(V, E) is said to be graceful if there exists an injection f : V(G) -> {0,1, . . . ,vertical bar E vertical bar}, such that the induced function f' : E (G) -> {1, 2, . . . , vertical bar E vertical bar} which is defined by f' (u, v) = (f(v) - f(u)) (mod vertical bar E vertical bar + 1) for every directed edge (u, v) is a bijection. Here, f is called a graceful labeling of D(V,E), and f' is called the induced edge's graceful labeling of D. In this paper we discuss the gracefulness of the digraph (P) over right arrow (a,b), and prove (P) over right arrow (a,b) is graceful if and only if both a and b are odd.