Odd Graceful Labeling of Some New Type of Graphs

Sushant Kumar Rout; Debdas Mishra; Purna chandra Nayak

doi:https://doi.org/10.14445/22315373/IJMTT-V41P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 41 | Number 1 | Year 2017 | Article Id. IJMTT-V41P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V41P502

Odd Graceful Labeling of Some New Type of Graphs

Sushant Kumar Rout, Debdas Mishra, Purna chandra Nayak

Citation :

Sushant Kumar Rout, Debdas Mishra, Purna chandra Nayak, "Odd Graceful Labeling of Some New Type of Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 41, no. 1, pp. 9-15, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V41P502

Abstract

In this paper some new type of odd graceful graphs are investigated. We prove that the graph obtained by joining a cycle C8 with some star graphs S1,r keeping one vertex and three vertices gap between pair of vertices of the cycle admits odd graceful labelling. We also prove that the graph obtained by joining a cycle C12 with some star graphs S1,r keeping two, three and five vertices gap between pair of vertices of the cycle admits odd graceful labelling. We observed that C8 ʘ S41,r with one vertex gap, C8 ʘ S21,r three vertices gap between pair of vertices of the cycle C8 are odd graceful , C12 ʘ S61,r with one vertex gap, C12 ʘ S41,r two vertices gap, C12 ʘ S31,r with three vertices gap and C12 ʘ S21,r with five vertices gap between pair of vertices are odd graceful graphs.

Keywords

Graceful labeling, graceful graphs, odd graceful graphs, star graphs.

References

[1]. F. Harary, “Graph Theory” – Addison Wesley, Reading Mass (1972).
[2]. S. Lo, On edge-graceful labelings of graphs, Congr. Numer., 50 (1985), pp. 231 – 241.
[3]. Sin-Min Lee, Kuo-Jye Chen and Yung-Chin Wang, On the edge-graceful spectra of cycles with one chord and dumbbell graphs .
[4] Rosa. A., 1967,”On certain valuation of the vertices of a graph theory of graphs”. Gordon and Breach.N.Y and Dunod Paris, pp. 349-355.
[5] R.B .Gnanajothi, Topics in graph theory,Ph.D Thesis,Madurai Kamraj University,Madurai,(1991).
[6] K.M. Kathiresan,Some classes of odd graceful graphs, ANJAC Journal of Sciences, 7(1)(2008).5-10.
[7] S K Vaidya, Lekha Bijukumar, “Odd Graceful Labeling of Some New Graphs” Published by Canadian Center of Science and Education, Vol. 4, No. 10; October 2010, pp. 65-70.
[8] S K Vaidya, N H Shah., “Graceful and odd Graceful Labeling of Some graphs” Published byInternational Journal of Mathematics and Soft Computing, Vol. 3, No.1, 2013, pp. 61-68.
[9] CHRISTIAN BARRIENTOS.,“ODD-GRACEFUL LABELINGS OF TREES OF DIAMETER 5” AKCE J.Graphs.Combin.,6,No 2 (2009),pp. 307-313.
[10]. J.A. Gallian, A dynamic survey of graph labeling, The electronic journal of Combinatorics, 16 (2015).