Induced Total Labellings of Models as Scale-free Networks


A recently discovered approach including de Brujin graphs and Eulerian circuits are used to DNA sequencing and fragment assembly, and to simplify DNA graphs through a series of transformations on graphs and digraphs in the field of bioinformatics. Since numbered graphs provide underlying mathematical models in studying the wide variety of seemingly unrelated practical applications, so graph colorings often are used to divide large systems into subsystems. A new graph labeling has been introduced and investigated.

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Yao, B. , Zhang, J. , Zhou, X. , Chen, X. , Zhang, X. , Yao, M. and Li, M. (2013) Induced Total Labellings of Models as Scale-free Networks. Communications and Network, 5, 65-68. doi: 10.4236/cn.2013.53B2013.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Jogen Bang-Jensen and Gregory Gutin, “Digraphs Theory, Algorithms and Applications,” Springer-Verlag. Berlin Heidelberg, New York, London, Paris, Tokyo, Hong Kong, Barcelona, Budapest, August 2007.
[2] G.S. Bloom and S.W. Golomb, “Applications of numbered undirected graphs,” Proc. IEEE, 65 (1977) 562-570. doi:10.1109/PROC.1977.10517
[3] J.A. Bondy and U.S.R. Murty, “Graph Theory with Application,” Macmillan, New York, 1976.
[4] Bela Bollobas and Oleg Pikhurko, “Integer Sets with Prescribed Pairwise Differences Being Distinct,” preprinted
[5] Hui Cheng, Bing Yao, Xiang-en Chen and Zhong-fu Zhang, “On Graceful Generalized Spiders and Caterpillars,”. Ars Combinatoria 87 (2008), 181-191.
[6] Joseph A. Gallian, “A Dynamic Survey of Graph Labeling,” The electronic journal of combinatorics, 14 (2009), # DS6.
[7] Jonathan Kaptcianos, “A Graph Theoretical Approach to DNA Fragment Assembly,” American Journal Of Undergraduate Research, VOL. 7, NO. 1 (2008)
[8] Ko-Wei Lih and Wei-Fan Wang, “Coloring The Square of An Outerplanar Graph,” Taiwanese Journal of Mathematics, Vol. 10, No. 4 (2006), 1015-1023.
[9] Pevzner P.A., Tang H., and Waterman M.S, “A New Approach to Fragment Assembly in DNA Sequencing,” RECOMB 01 (2001), 256-267. doi:10.1145/369133.369230
[10] Alexander Rosa, “On certain valuations of the vertices of a graph,” Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967), 349-355.
[11] J. Topp and P.D. Vestergaard, “\alpha_k$- and $\gamma_k$-stable graphs,” Discrete Mathematics 212 (2000), 149-160. doi:10.1016/S0012-365X(99)00216-2
[12] Yao Bing, Ming Yao, Hui Cheng, Jin-wen Li, Ji-guo Xie and Zhong-fu Zhang, “On Felicitous Labelling of Trees,” Proceeding of The 4th International Workshop on Graph Labeling (IWOGL 2008), Harbin Engineering University and University of Ballarat, Australia, January, 2008, 5-8.
[13] Bing Yao, Hui Cheng, Ming Yao and Meimei Zhao, “A Note on Strongly Graceful Trees,” Ars Combinatoria 92 (2009), 155-169.
[14] Bing Yao, Ming Yao and Hui Cheng, “On Generalized Antiaverage Problem,” Ars Combinatoria Volume XCVI, July, 2010.

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