Some New Classes of Graceful Lobsters

Dedas Mishra¹ , Amaresh Chandra Panda² , Subarna Bhattacharjee³

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.6 , pp.30-39, Dec-2021

Online published on Dec 31, 2021

Copyright © Dedas Mishra, Amaresh Chandra Panda, Subarna Bhattacharjee . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
It is readily found that a lobster L contains a unique path, say P = x_0 x_1?x_n called as the central path of L such that each vertex x_i,0

Key-Words / Index Term :
graceful labeling, lobster, central path odd, even and pandent branches

References :
[1] A. Rosa, “On Certain Valuations of the Vertices of a Graph, Theory of Graphs,” In the Proceedings of International Symposium, Rome, Gordon and Breach, N. Y. and Dunod Paris, pp. 349-355, 1966.
[2] J. C. Bermond, “Radio Antennae and French Windmills”, Graph Theory and Combinatorics, In Research Notes in Maths, (ed.R.J. Wilson), Vol. 34, pp. 18 – 39, 1979.
[3] J.A. Gallian, “A Dynamic Survey of Graph Labeling”, Electronic Journal of Combinatorics, DS6, 23nd edition, December 17, 2020.
[4] H. K. Ng, Gracefulness of a Class of Lobsters”, Notices AMS, Vol. 7, Abstract No. 825-05-294, 1986.
[5] J.G. Wang, D. J. Jin, X.-G Lu, and D. Zhang, “The Gracefulness of a Class of Lobster Trees”, Mathematical Computer Modeling, Vol.20, pp. 105-110, 1994.
[6] S. L. Zhao, “All Trees of Diameter Four are Graceful,” Ann. New York Acad. Sci., Vol. 576, pp. 700 – 706, 1989.
[7] P. Hrnciar and A. Havier, “All Trees of Diameter Five Are Graceful”, Discrete Mathematics, Vol.233, pp. 133-150, 2001.
[8] C. Huang, A. Kotzig, and A. Rosa, “Further Results on Tree Labellings”, Util. Math., Vol.21, pp.31-48, 1982.
[9] D. Morgan, “All Lobsters with Perfect Matching are Graceful”, Electron. Notes Discrete Math., Vol. 1, pp. 6, 2002.
[10] W. C. Chen, H. I. Lu, and Y. N. Lu, “Operations of Interlaced Trees and Graceful Trees”, South East Asian Bulletin of Mathematics, Vol. 4, pp. 337 – 348, 1997.
[11] D. Mishra, P. Panigrahi, “Some Graceful Lobsters with All Three Types of branches Incident on the Vertices of the Central Path”, Computers and Mathematics with Applications, Vol. 50, Issue. 4, pp. 367-380, 2005.
[12] D. Mishra and P. Panigrahi, “Graceful Lobster Obtained by Component Moving of Diamater Four Trees”, Ars Combinatoria, Vol. 89, pp. 129-147, 2006.
[13] D. Mishra and P. Panigrahi, “Some Graceful Lobsters with Both Odd and Even Degree Vertices on Central Path”, Utilitus Mathematics, Vol.74, pp.155-177, 2007.
[14] D. Mishra and P. Panigrahi, “Some Graceful Lobsters with All Three Types of Branches Incident on the Vertices of the Central Path”, Computers and Mathematics with Applications, Vol. 56, pp. 1382 – 1394, 2008.
[15] D.Mishra and P. Panigrahi, “Graceful Lobsters Obtained from Diameter Four Trees Using Partitioning Technique”, Ars Combinatoria, Vol. 87 , pp. 291 – 320, 2008.
[16] D. Mishra and P. Panigrahi, “A New Class of Graceful Lobsters Obtained from Diameter Four Trees,” Utilitus Mathematica, Vol. 80 pp. 183 – 209, 2009.
[17] D. Mishra and P. Panigrahi, “Some New Classes of Graceful Lobsters Obtained from Diameter Four Trees”, Mathematica Bohemica, Vol. 135, No. 3, pp. 257 – 278, 2010.
[18] D. Mishra and P. Panigrahi, “Some New Classes of Graceful Lobsters Obtained by Applying Inverse And Component Moving Transformations”, International Journal of Mathematics Trends and Technology (IJMTT), Vol.1, Issue – 2, pp. 6 – 16, 2011.
[19] P. Panigrahi and D. Mishra, “Graceful Lobsters Obtained from Diameter Four Trees Using Partitioning Technique”, ARS Combinatoria, Vol. 87, pp. 291- 320, 2008.
[20] P. Panigrahi and D.Mishra, “Larger Graceful and Interlaced Lobster Obtained by Joining Smaller Ones”, South East Asian Bulletin of Mathematics, Vol. 33, pp. 509-525, 2009.
[21] D. Mishra, A. C. Panda, and R. B. Dash, “A Class of Graceful Lobsters with Even Number of Branches Incident on the Central Path”, International Journal of Mathematical Sciences and Applications, Vol. 1, No. 2, pp. 463 – 472, 2011.
[22] D. Mishra and A. C. Panda, “Some New Graceful Generalized Classes of Lobsters”, International Journal of Pure and Applied Mathematics (IJPAM), ISSN: 1311-8080, Volume – 91, Issue. 1, pp. 57 – 76, 2014.
[23] D. Mishra and A. C. Panda, “Some New Family of Graceful Lobsters”, Advances and Applications in Discrete Mathematics (AADM), Volume 14, Issue. 1, pp. 1-24, 2014.
[24] D. Mishra and S. Bhattacharjee, “Some New Classes of Lobsters Exhibiting Graceful Labeling”, Global Journal of Pure and Applied Mathematics, Volume 11, No- 2, pp. 909 – 930, 2015.
[25] D. Mishra, S. K. Rout, P. C. Nayak, “Some New Graceful Lobsters with Pendant Vertices with Central Paths”, Indian Journal of Science and technology, Vol 10, Issue. 6, pp. 1-9, 2017.
[26] G. Sethuraman and J. Jesintha, “A New Class of Graceful Lobsters”, J. .Combin. Math. Combin. Computing, Vol. 67, pp.99-109, 2008.
[27] S. Ghosh, “On Certain Classes of Graceful Lobsters,” Ars Combin., Vol. 136, pp. 67 – 96, 2018.
[28] D. Mishra, S. K. Rout, S. Bhattacharjee, “Some New Classes of K-Distance Trees with Alpha Labeling,” International Journal of Scientific Research in Mathematical and Statistical Sciences, E-ISSN: 2348-4519, Vol 7, Issue 4, pp. 26 - 34 , 2020.
[29] J. Jeba Jesintha, R. Jayaglory, G. Bhabita, Odd Graceful Labelling of the Union of Cycle and Lobsters, International Journal of Computer Sciences and Engineering, Vol.-7, Special Issue, 5,pp. 59-63, 2019.