Odd graceful labeling for the jewel graph and the extended jewel graph without the prime edge ∗

J Jeba Jesintha; N K Vinodhini; Shahina Munavar  Hussain

doi:10.48165/

Authors

J Jeba Jesintha P.G. Department of Mathematics, Women’s Christian College, Chennai, Tamil Nadu, India.
N K Vinodhini Department of Mathematics, Anna Adarsh College for Women, Chennai, Tamil Nadu, India.
Shahina Munavar Hussain P.G. Department of Mathematics, Women’s Christian College, Chennai, Tamil Nadu, India.

DOI:

https://doi.org/10.48165/

Keywords:

Odd graceful labeling, Jewel graph, Extended Jewel graph

Abstract

R.B. Gnanajothi (Topics in Graph Theory, Ph.D. Thesis, Madurai Kamaraj University, Madurai, Tamil Nadu, India, 1991) introduced odd graceful labeling. A func tion f is called an odd graceful labeling of a graph G if f : V (G) → {0, 1, 2, ..., 2q − 1} is injective and the induced function f∗: E(G) → {1, 3, ..., 2q − 1} defined as f∗(e = uv) = |f(u) − f(v)| is bijective. A graph which admits an odd graceful labeling is called an odd graceful graph. Many results exist on odd graceful labeling. The concept of odd graceful labeling is implemented in the areas of coding theory.

In this paper we prove that the jewel graph J∗n and the extended jewel graph EJ∗n,m without the prime edge is odd graceful.

References

Jeba Jesintha, J. and Ezhilarasi Hilda, K. (2014), Sub divided shell flower graphs are odd graceful, International Journal of Innovation in Science and Mathematics, 2(4),

Gallian, J.A. (2018). A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 73–76.

Gnanajothi, R.B. (1991). Topics in Graph Theory, Ph.D. Thesis, Madurai Kamaraj University, Madurai, Tamil Nadu, India.

Kathiresan, K.M (2008). Some classes of odd graceful graphs, ANJAC Journal of Sciences, 7(1), 5–10.

Moussa, M.I. and Badr, E.M. (2009). Odd graceful labeling of crown graphs, International Con ference on Computer Science from Algorithms to Applications, Cairo, Egypt. [6] Rosa, A. (1967). On certain valuations of the vertices of a graph, Theory of Graphs (International Symposium, Rome, July 1966), Gordon and Breach, N.Y. and Dunod Paris, 349-fi355. [7] Sekar, C. (2002). Studies in graph theory, Ph. D Thesis, Madurai Kamaraj University, Madurai, Tamil Nadu, India.