文章摘要
把丽娜,刘倩,刘信生,姚兵.完全二部图优美性质探索[J].,2017,57(6):657-662
完全二部图优美性质探索
Exploration of gracefulness of some complete bipartite graphs
  
DOI:10.7511/dllgxb201706016
中文关键词: 树  完全二部图  优美标号  (k,d)-优美标号
英文关键词: trees  complete bipartite graph  graceful labelling  (k,d)-graceful labelling\@
基金项目:国家自然科学基金资助项目(61163037,61163054,61363060)
作者单位
把丽娜,刘倩,刘信生,姚兵  
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中文摘要:
      图论的二部图及其标号在实际应用中较多,尤其最近图标号被应用于新型的图形密码设计.首先构造出了组合完全二部图与串联完全二部图,发现了一种叫做奇边魔幻全标号的标号,并给出了组合完全二部图具有奇边魔幻全标号的证明.此外,得出了串联完全二部图是优美图、(k,d)-优美图的结论.
英文摘要:
      The bipartite graphs of graph theory and graph labellings are widely used in practical applications, especially recently the graph labelling has been applied to design a new type of graphical password. Firstly, some complete bipartite graphs are constructed by combinatoric and series methods. A new labelling, called edge-odd-magical total labelling, is found and it is proved that the combinatoric complete bipartite graphs admit the edge-odd-magical total labelling. Moreover, series complete bipartite graphs are graceful, or (k,d)-graceful.
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