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graceful labeling; lobster; odd branch; even branch; inverse transformation; component moving transformation

References:

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[6] Mishra, D., Panigrahi, P.: **Graceful lobsters obtained by component moving of diameter four trees**. Ars Combinatoria 81 (October, 2006) 129-146. MR 2267807 | Zbl 1189.05154

[7] Mishra, D., Panigrahi, P.: **Graceful lobsters obtained by partitioning and component moving of diameter four trees**. Computers and Mathematics with Applications 50 (August 2005) 367-380. DOI 10.1016/j.camwa.2005.04.006 | MR 2165426

[8] Morgan, D.: **All lobsters with perfect matchings are graceful**. Technical Report, University of Alberta, TR05-01, Jan 2005.\hfil url: http://www.cs.ualberta.ca/research/techreports/2005.php Zbl 1169.05374

[9] Ng, H. K.: **Gracefulness of a class of lobsters**. Notices AMS 7 (1986), abstract no. 825-05-294.

[10] Panigrahi, P., Mishra, D.: **Graceful lobsters obtained from diameter four trees using partitioning technique**. Ars Combinatoria 87 (April, 2008) 291-320. MR 2414024

[11] Ringel, G.: **Problem 25 in theory of graphs and applications**. Proceedings of Symposium Smolenice 1963, Academia (1964), 162.

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[13] Wang, J. G., Jin, D. J., Lu, X. G., Zhang, D.: **The gracefulness of a class of lobster trees**. Math. Comput. Modelling 20 (1994), 105-110. DOI 10.1016/0895-7177(94)00167-7 | MR 1302631 | Zbl 0814.05063