Release Time:2019-03-11  Hits:

Indexed by: Journal Article

Date of Publication: 2009-01-01

Journal: Ars Combinatoria

Included Journals: Scopus

Volume: 92

Page Number: 419-428

ISSN: 03817032

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  m and prove that n - C  m is a graceful digraph for m = 4,6,8,10 and even n.