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On Odd Graceful Labeling of the Generalization of Cyclic Snakes

by E. M. Badr
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 106 - Number 12
Year of Publication: 2014
Authors: E. M. Badr
10.5120/18574-9825

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 },
issue_date = { November 2014 },
volume = { 106 },
number = { 12 },
month = { November },
year = { 2014 },
issn = { 0975-8887 },
pages = { 26-32 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume106/number12/18574-9825/ },
doi = { 10.5120/18574-9825 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:39:14.581657+05:30
%A E. M. Badr
%T On Odd Graceful Labeling of the Generalization of Cyclic Snakes
%J International Journal of Computer Applications
%@ 0975-8887
%V 106
%N 12
%P 26-32
%D 2014
%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
  1. R. B. Gnanajothi, Topics in graph theory, Ph. D. thesis, Madurai Kamaraj University, India, 1991.
  2. J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, (http://www. combinatorics. org/) DS 16 (2013).
  3. E. M. Badr and M. I. Moussa, ODD GRACEFUL LABELINGS OF CYCLIC SNAKES , Electronic Journal of Nonlinear Analysis and Application, Vol. 6, December 2012.
  4. 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
  5. 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
  6. A. Rosa, Cyclic Steiner Triple Systems and Labeling of Triangular Cacti, Scientia, 5 (1967) 87-95.
  7. 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.
  8. 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
  9. Christian Barrientos, Graceful labelings of cyclic snakes, Ars Combinatorica 60 (2001), pp. 85-96.
  10. 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
Index Terms

Computer Science
Information Sciences

Keywords

Graph Labeling Odd Graceful Graphs Cyclic Snakes

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