Research Article
On Odd Graceful Labeling of the Generalization of Cyclic Snakes
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 106 - Issue 12 |
| Published: November 2014 |
| Authors: E. M. Badr |
10.5120/18574-9825
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E. M. Badr . On Odd Graceful Labeling of the Generalization of Cyclic Snakes. International Journal of Computer Applications. 106, 12 (November 2014), 26-32. DOI=10.5120/18574-9825
@article{ 10.5120/18574-9825,
author = { E. M. Badr },
title = { On Odd Graceful Labeling of the Generalization of Cyclic Snakes },
journal = { International Journal of Computer Applications },
year = { 2014 },
volume = { 106 },
number = { 12 },
pages = { 26-32 },
doi = { 10.5120/18574-9825 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2014
%A E. M. Badr
%T On Odd Graceful Labeling of the Generalization of Cyclic Snakes%T
%J International Journal of Computer Applications
%V 106
%N 12
%P 26-32
%R 10.5120/18574-9825
%I Foundation of Computer Science (FCS), NY, USA
Abstract
The objective of this paper is to present a new class of odd graceful graphs. In particular, we show that the linear cyclic snakes (1, k) C4- snake and (2, k) C4- snake are odd graceful. We prove that the linear cyclic snakes (1, k) C6- snake and (2, k) C6- snake are odd graceful. We also prove that the linear cyclic snakes (1, k) C8- snake and (2, k) C8- snake are odd graceful. We generalize the above results "the linear cyclic snakes (m, k) C4- snake, (m, k) C6-snake and (m, k) C8-snake are odd graceful ". Finally, we introduce a new conjecture" All the linear cyclic snakes (m, k) Cn-snakes are odd graceful if n is even)".
References
- R. B. Gnanajothi, Topics in graph theory, Ph. D. thesis, Madurai Kamaraj University, India, 1991.
- J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, (http://www. combinatorics. org/) DS 16 (2013).
- E. M. Badr and M. I. Moussa, ODD GRACEFUL LABELINGS OF CYCLIC SNAKES , Electronic Journal of Nonlinear Analysis and Application, Vol. 6, December 2012.
- E. M. Badr ( 2014), On the Odd Gracefulness of Cyclic Snakes With Pendant Edges, International journal on applications of graph theory in wireless ad hoc networks and sensor networks (GRAPH-HOC) Vol. 4, No. 4, December 2012
- E. M. Badr ( 2014), Odd Graceful Labeling of the revised friendship graphs, International Journal of Computer Applications (0975 – 8887) Volume 65– No. 11, March 2013
- A. Rosa, Cyclic Steiner Triple Systems and Labeling of Triangular Cacti, Scientia, 5 (1967) 87-95.
- E. M. Badr and M. E. Abdel-aal, Odd Graceful Labeling for the Subdivision of Double Triangles Graphs, International Journal of Soft Computing, Mathematics and Control (IJSCMC), Vol. 2, No. 1, February 2013.
- E. M. Badr and M. E. Abdel-aal, ( 2013), ODD GRACEFULL LABELING FOR THE SUBDIVISON OF DOUBLE TRIANGLES GRAPHS, International Journal of Soft Computing, Mathematics and Control (IJSCMC), Vol. 2, No. 1, February 2013
- Christian Barrientos, Graceful labelings of cyclic snakes, Ars Combinatorica 60 (2001), pp. 85-96.
- E. M. Badr ( 2014), Complete Reference for Odd Graceful Labeling of Cyclic Snakes,Technical Report 2, 2014, Benha Unveristy, Faculty of Computers and Informatics, http://www. bu. edu. eg/staff/alsayedbadr7
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