Super vertex mean labeling of cycles through different ways

  • A. Lourdusamy St. Xaviers College (Autonomous)
  • Sherry George St. Xaviers College (Autonomous)

Resumen

A super vertex mean labeling f of a (p, q) - graph G = (V,E) is defined as an injection from E to the set {1, 2, 3, ··· , p + q} that induces for each vertex v the label defined by the rule fv(v) = Round  , where Ev denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1, 2, 3, ··· , p + q}. In this paper, we investigate the super vertex mean labeling behavior of cycles by giving various ways by which they can be labeled.

Biografía del autor

A. Lourdusamy, St. Xaviers College (Autonomous)
Departmento de Matemáticas.
Sherry George, St. Xaviers College (Autonomous)
Departmento de Matemáticas.

Citas

[1] B. D. Acharya and K. A. Germina, Vertex-graceful Graphs, Journal of Discrete Mathematical Science and Chryptography, 13 (5), pp. 453-463, (2010).

[2] J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, 16, (2013).

[3] S. W. Golomb, How to Number a Graph, Graph Theroy and Computing (Ed.R.C.Read), Academic Press, New York, pp. 23-27, (1972).

[4] R. L. Graham and N. J. A. Solane, On additive Bases and Harmonious Graphs, SIAM, J.Alg. Discrete Methods, 1, pp. 382-404, (1980).

[5] A. Lourdusamy and M. Seenivasan, Vertex-mean Graphs, International Journal of Mathematical Combinatorics, 3, pp. 114-120, (2011).

[6] A. Lourdusamy and M. Seenivasan, Mean Labelings of Cyclic Snakes, AKCE International Journal of Graphs and Combinatorics, 8 (2), pp. 105-113, (2011).

[7] A. Lourdusamy, M. Seenivasan, Sherry George and R.Revathy, Super Vertex-Mean Graphs, Sciencia Acta Xaveriana, 5 (2), pp. 39-46, (2014).

[8] R. Ponraj. Studies in Labelings of Graphs, Ph.D.thesis, Manonmaniam Sundaranar University, India, (2004).

[9] R. Ponraj and D. Ramya, On Super Mean Graphs of Order 5, Bulletin of Pure and Applied Sciences 25 (1), pp. 143-148, (2006).

[10] D. Ramya, R. Ponraj, and P. Jeyanthi, Super Mean Labeling of Graphs, Ars Combin., 112, pp. 65-72, (2013).

[11] A. Rosa, On Certain Valuations of the Vertices of a Graph,in: Theory of Graphs (International Symposium, Rome, July 1966; Gordon and Breach, N.Y. and Dunod Paris, pp. 349-355, (1967).

[12] M. Seenivasan, Studies in Graph Theory; Some New Labeling Concepts, Ph. D. thesis, Manonmaniam Sundaranar University, India, (2013).

[13] S. Somasundaram and R. Ponraj, Super Mean Labeling of Graphs, National Academy, Science Letters, 26, pp. 210-213, (2003).

[14] R. Vasuki and A. Nagrajan, Some Results on Super Mean Labeling of Graphs, International Journal of Mathematical Combinatorics, 3, pp. 82-96, (2009).

[15] D. B. West, Introduction to Graph Theory, Prentice-Hall of India, Private Limited, New Delhi, (1996).
Publicado
2018-06-05
Cómo citar
Lourdusamy, A., & George, S. (2018). Super vertex mean labeling of cycles through different ways. Proyecciones. Journal of Mathematics, 37(2), 181-198. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2921
Sección
Artículos