Some Results on Vertex Equitable Labeling

DOI: 10.4236/ojdm.2012.22009   PDF   HTML   XML   4,794 Downloads   8,966 Views   Citations


Let G be a graph with p vertices and q edges and let A= vertex labeling is said to be a vertex equitable labeling of G if it induces an edge labeling given by such that and , where is the number of vertices v with for A graph G is said to be a vertex equitable graph if it admits vertex equitable labeling. In this paper, we establish the vertex equitable labeling of a Tp-tree, where T is a Tp-tree with even number of vertices, bistar the caterpillar and crown

Share and Cite:

P. Jeyanthi and A. Maheswari, "Some Results on Vertex Equitable Labeling," Open Journal of Discrete Mathematics, Vol. 2 No. 2, 2012, pp. 51-57. doi: 10.4236/ojdm.2012.22009.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] G. Bloom and S. Ruiz, “Decomposition into Linear Forest and Difference Labelings of Graphs,” Discrete Applied Mathematics, Vol. 49, 1994, pp. 61-75. doi:10.1016/0166-218X(94)90201-1
[2] J. A. Gallian, “A Dynamic Survey of Graph Labeling,” The Electronic Journal of Combinatorics, Vol. 18, 2011, Paper #DS6.
[3] F. Harary, “Graph Theory,” Addison Wesley, Massachusetts, 1972.
[4] R. Ponraj and S. Somasundram, “Mean Labeling of Graphs,” National Academy Science Letters, Vol. 26, 2003, pp. 210-213.
[5] R. Ponraj and S. Somasundram, “Non-Existence of Mean Labeling for a Wheel,” Bulletin of Pure and Applied Sciences (Mathematics & Statistics), Vol. 22E, 2003, pp. 103-111.
[6] R. Ponraj and S. Somasundram, “Some Results on Mean Graphs,” Pure and Applied Mathematical Sciences, Vol. 9, 2004, pp. 47-58.
[7] R. Ponraj and S. Somasundram, “Further Results on Mean Graphs,” Proceedings f SACOEFERENCE, National Level Conference, Dr. Sivanthi Aditanar College of Engineering, 2005, pp. 443-448.
[8] M. Seenivasan and A. Lourdusamy, “Vertex Equitable Labeling of Graphs,” Journal of Discrete Mathematical Sciences & Cryptography, Vol. 11, No. 6, 2008, pp. 727- 735.
[9] S. M. Hegde and S. Shetty, “On Graceful Trees,” Applied Mathematics E-Notes, Vol. 2, 2002, pp. 192-197.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.