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论文类型：期刊论文

发表时间：2012-06-01

发表刊物：CZECHOSLOVAK MATHEMATICAL JOURNAL

收录刊物：SCIE、Scopus

卷号：62

期号：2

页面范围：527-539

ISSN号：0011-4642

关键字：cubic mapping graph; cycle; height

摘要：Let a"currency sign (n) [i] be the ring of Gaussian integers modulo n. We construct for a"currency signn[i] a cubic mapping graph I"(n) whose vertex set is all the elements of a"currency signn[i] and for which there is a directed edge from a a a"currency signn[i] to b a a"currency signn[i] if b = a (3). This article investigates in detail the structure of I"(n). We give suffcient and necessary conditions for the existence of cycles with length t. The number of t-cycles in I"(1)(n) is obtained and we also examine when a vertex lies on a t-cycle of I"(2)(n), where I"(1)(n) is induced by all the units of a"currency signn[i] while I"(2)(n) is induced by all the zero-divisors of a"currency signn[i]. In addition, formulas on the heights of components and vertices in I"(n) are presented.