Felicitous Labellings of Some Network Models

Jiajuan Zhang, Bing Yao, Zhiqian Wang, Hongyu Wang, Chao Yang, Sihua Yang

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China.
School of Mathematics Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China.

DOI: 10.4236/jsea.2013.63B007                

Abstract

Building up graph models to simulate scale-free networks is an important method since graphs have been used in researching scale-free networks. One use labelled graphs for distinguishing objects of communication and information networks. In this paper some methods are given for constructing larger felicitous graphs from smaller graphs having special felicitous labellings, and some network models are shown to be felicitous.

Keywords

Felicitous Labelling; Set-Ordered Felicitous Labelling; Symmetric Graphs;Trees

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. A. Gallian. A Dynamic Survey of Graph Labeling. The lec-tronic journal of combinatorics, 17 (2010), # DS6.
[2]	Graham R J, Sloane N J A. On additive bases and harmonious graphs. SIAM J Algebraic Discrete Mathods, 29(1) (1980), 382-404.
[3]	Rikio Ichishma and Akito Oshima. On partitional and other related graphs. preprint.
[4]	Li L., Al-derson D., Tanaka R., Doyle J.C., and Willinger, W. Towards A Theory Of Scale-Free Graphs: Definition, Properties, And Implications. Internet Mathematics 2 (4) (2005), 431-523.
[5]	Bing Yao, Ming Yao, Hui Cheng, Jin-wen Li, Ji-guo Xie and Zhong-fu Zhang. On Felicitous Labelling of Trees. The proceeding of The 4th International Workshop on Graph Labeling (IWOGL 2008), Harbin Engineering University and University of Ballarat, Australia, January, 2008. pp5-8.
[6]	Bing Yao, Xiang'en Chen, Ming Yao, Hui Cheng. On (k, ?)-magically total labeling of graphs. submitted to JCMCC.
[7]	Bing Yao, Hui Cheng, Ming Yao and MeiMei Zhao. A Note on Strongly Graceful Trees. Ars Combinatoria 92 (2009), 155-169.
[8]	Xiangqian Zhou, Bing Yao, Xiang'en Chen, and Haixia Tao. A proof to the odd-gracefulness of all lobsters. Ars Combinatoria, Volume CIII, January (2012),13-18.
[9]	Bing Yao, Xiang'en Chen, Xiangqian Zhou,Jiajuan Zhang, Xiaomin Zhang, Ming Yao, Mogang Li, Jianming Xie. Graphs Related With Scale-free Networks. Pro-ceeding of The 2nd International Conference on Electronics, Communications and Control (ICECC2012), October, 2012, Zhoushan, China, 284-287.