摘要
主要讨论无向图G的Mycielskian图μ()G的超欧拉性和强连通有向图D的Mycielskian图μ(D)的欧拉性及超欧拉性的问题,通过灵活运用综合法和反证法两种数学方法,使得问题得以解决。给出了无向图G的Mycielskian图μ(G)是超欧拉无向图的证明,强连通有向图D的Mycielskian有向图μ(D)是欧拉有向图的充要条件及强连通有向图D的Mycielskian有向图μ(D)是超欧拉有向图的充要条件。通过对这些问题的讨论和证明,可以拓宽人们对Mycielskian(有向)图的性质更进一步的认识及了解,以便今后实际中能够更好利用Mycielskian图的性质。
This paper mainly discusses about the problem of the Supereulerian property of Mycielskian graphμ(G)of graph G and the problem of Euler property and Supereulerian property of Mycielskian digraphμ(D)of strong digraph D.These problems are solved by the method of synthesis and proof by contradiction.In this paper,the Mycielskian graphμ(G)of the graph G is proved to be a Supereulerian graph,and the necessary and sufficient conditions for a Mycielskian digraphμ(D)of strong digraph D to be Euler digraph and Supereulerian digraph are also given.by discussing and proving these problems,it is hoped that the nature of Mycielskian(di)graphs can be further understood and put into better use in the future.
作者
郑焕
刘娟
ZHENG Huan;LIU Juan(College of Mathematical Sciences,Xinjiang Normal University,Urumqi Xinjiang 830017,China)
出处
《西华师范大学学报（自然科学版）》
2017年第4期405-409,共5页
Journal of China West Normal University(Natural Sciences)
基金
国家自然科学基金(61363020)
新疆师范大学硕士研究生科技创新项目(XSY201602013)
