Some Results on Vertex Equitable Labeling

Affiliation(s)

Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur, India.

Department of Mathematics, Kamaraj College of Engineering and Technology, Virudhunagar, India.

Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur, India.

Department of Mathematics, Kamaraj College of Engineering and Technology, Virudhunagar, India.

ABSTRACT

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

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

Cite this paper

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.

P. Jeyanthi and A. Maheswari, "Some Results on Vertex Equitable Labeling,"

References

[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.

[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.