Proper Lucky Number of Hexagonal Mesh and Honeycomb Network

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-48 Number-4
Year of Publication : 2017
Authors : D. Antony Xavier, R.C. Thivyarathi
  10.14445/22315373/IJMTT-V48P532

MLA

D. Antony Xavier, R.C. Thivyarathi "Proper Lucky Number of Hexagonal Mesh and Honeycomb Network", International Journal of Mathematics Trends and Technology (IJMTT). V48(4):223-228 August 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
Let G V, E be a graph with vertex set V and edge set E. Let f be a labeling defined in G.

Reference
1. L. Addhario- Berry, R.E.L.Aldred, K.Dalai, B.A. Reed, “Vertex coloring edge partitions”, Journal of combinatorial Theory series, vol 94 n.2, p 237-244, July 2005.
2. A. Ahai, A. Dehghan, M. Kazemi, E. Mollaahmedi, “Computation of Lucky number of planar graphs is NP-hard”, Information processing letters, vol 112, Iss 4, p 109-112, 15th Feb 2012.
3. S. Akhari, M. Ghanbari, R. Manariyat, S. Zare, „ On the lucky choice number of graphs”, Graphs and combinatorics, vol 29 n.2, p 157-163, Mar 2013.
4. G. Chartand, F.Okamoto, P.Zhang, “The sigma chromatic number of a graph”, Graphs and combinatorics 26 (6), p 755- 773, 2010.
5. Czerwinski, Sebastian, Grytczuk, Jaroslaw, Elazny and Wiktor, “ Luckylabeling of graphs”, Inf. Process. Lett. 109(18); 1078-1081. Zbl 1197.05125, 2009.
6. A. Dehghan, M.R. Sadeghi, A. Ahadi, “ Algorithmic complexity of proper labeling problems”, Theoretical computer science, vol 495, p 25-36, 2013.
7. J.Gallian, “ A Dynamic survey of graph labeling,” The Electronic journal of combinatorics, 1996- 2005.
8. Y.Kins, R.C. Thivyarathi, D.Antony Xavier, “ Proper Lucky number of Mesh derived aricheture”,
9. LeenaSankari S., Masthan K.M.K., AravindhaBabu N., Bhattacharjee T., Elumalai M., "Apoptosis in cancer - an update", Asian Pacific Journal of Cancer Prevention, ISSN : 1513-7368, 13(10) (2012) PP. 4873-4878.
10. Michal Karonski, Tomasz Luczak, Andrew Thomason, “Edge weights and vertex colors”, Journal of combinatorics theory series B, vol 91n.1, p151-157, May 2004.
11. A. NellaiMurugan, R. Maria Irudhaya Aspin Chitra, “Lucky Edge Labeling of Pn, Cn and Corona of Pn, Cn”, IJSIMR, Volume 2, Issue 8, August 2014, pp. 710-718
12. S. Ramachandran and S.Arumugam, „Invitation to graph theory‟, Scitech publication pvt.Ltd, Reprint, Jan 2009.
13. Subhashree A.R., Parameaswari P.J., Shanthi B., Revathy C., Parijatham B.O., "The reference intervals for the haematological parameters in healthy adult population of Chennai, Southern India", Journal of Clinical and Diagnostic Research, ISSN : 0973 - 709X, 6(10) (2012), PP. 1675-1680.
14. Sharieh A, Qatawneh M, Almobaideen W, Sleit A, “Hex-Cell: Modeling, Topological Properties and Routing Algorithm”, European Journal of Scientific Research, ISSN 1450-216X Vol. 22 No.2 , 457-468, (2008).

Keywords
Lucky labeling, Proper lucky number, Hexagonal mesh and Honeycomb network.