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Indexed by:期刊论文

Date of Publication:2010-03-01

Journal:UTILITAS MATHEMATICA

Included Journals:SCIE、Scopus

Volume:81

Page Number:255-264

ISSN No.:0315-3681

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, ... , 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 (graceful numbering) 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 n.(C) over right arrow (m) and prove a conjecture that the digraph n.(C) over right arrow (m) is a graceful digraph for any odd m and even n.