Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2009-07-01

Journal: ARS COMBINATORIA

Included Journals: SCIE

Volume: 92

Page Number: 419-428

ISSN: 0381-7032

Key Words: Digraph; Directed Cycles; Graceful Graph; Graceful Labeling

Abstract: A digraph D(V, E) is said to be graceful if there exists an injection f : V(G) -> {0, 1, ... , |E|} such that the induced function f' : E(G) -> {1, 2, ... , |E|} which is defined by f' (u, v) = [f(v)-f(u)] (mod |E| + 1) for every directed edge (u, v) is a bijection. Here, f is called a graceful labeling (graceful numbering) of D(V, E), while f' is called the induced edge's graceful labeling of D. In this paper we discuss the gracefulness of the digraph n - (C) over right arrow (m) and prove that n - (C) over right arrow (m) is a graceful digraph for m = 4, 6, 8, 10 and even n.