Journal of East China Normal University(Natural Sc

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A new method for proving strongly (k, d)-graceful trees

ZHAO Xi-yang, WANG Xiao-min, YAO Bing   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
  • Received:2015-06-24 Online:2016-07-25 Published:2016-09-29


In investigating graph graceful problem that has many applications in the real world, we discovery a new method called the appending-split method. By this new
method we can construct large scale of trees having strongly (k, d)-graceful labellings, and provide the proof for the correctness of constructed (k, d)-graceful trees. Furthermore, such strongly (k, d)-graceful labellings can induce strongly odd-graceful labellings. Our new method can be easily transformed into a good algorithm that may be a theoretical guarantee for applying strongly (k, d)-graceful labellings to network.

Key words: strongly (k, d)-graceful labelling, strongly odd-graceful labelling, perfect matching