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论文类型：期刊论文

发表时间：2010-03-01

发表刊物：UTILITAS MATHEMATICA

收录刊物：SCIE、Scopus

卷号：81

页面范围：255-264

ISSN号：0315-3681

关键字：Digraph; Directed Cycles; Graceful Graph; Graceful Labeling

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 (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.