Super Magic of Some Connected Graphs Pn * 2nP2 , Pn * 2nP3, Pn * 2nP4, and Pn * 2nP5

A. Solairaju; S. Malathi

doi:https://doi.org/10.14445/22315373/IJMTT-V54P550

International Journal of Mathematics Trends and Technology

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Volume 54 | Number 5 | Year 2018 | Article Id. IJMTT-V54P550 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P550

Super Magic of Some Connected Graphs Pn * 2nP2 , Pn * 2nP3, Pn * 2nP4, and Pn * 2nP5

A. Solairaju, S. Malathi

Abstract

Neelam Kumari, and Seema Mehra [2013] gave the contributions (1) Pt admits n-edge magic labeling for all positive integer t; (2) Ct admits n-edge magic labeling when t is even; (3) A sun graph St is n-edge magic only when t is even; (4) If G admits n-edge magic labeling, then G + K1 admits n-edge magic labeling; and (5) Let Sm, t be a double star graph, then the graph Sm, t admits n-edge magic labeling. Antony Xavier [2014] verified (1) Let G be a graph. If G has a vertex magic total labeling then it has a modular super vertex magic labelling. But converse need not be true;(2) Km,m has no modular super vertex magic total labeling; (3) IfG is a star graph with odd number of vertices then there exist a modular super vertex magic total labeling with k = 1. Ponnappan, Nagaraj, and Prabakaran [2014] found (1)Let G be a nontrivial graph G with m ≥ n-1 is odd vertex magic labeling then the magic constant k is given by k =3n-2 when m = n-1 otherwise k = 1 + 2m + otherwise k = 1 + 2m +(m2 +m)/n; (2) A cycle Cn is odd vertex magic labeling iff n is odd;(3) A path Pn is odd super vertex magic labeling if and only if n is odd and n≥ 3; (4) All n-suns are not odd vertex magic labelling. The aim of the paper is to find super magic labelings for the graphs2nP2 , Pn * 2nP3, Pn * 2nP4, and Pn * 2nP5.

Keywords

Magic graph, super magic graph.

References

1. Antony Xavier, D., Modular Super vertex magic total labelling, International Journal of Computing Algorithm, Volume: 3, 606-608, February 2014.
2. Jayapal Baskar Babujee, and Babitha Suresh, New Constructions of Edge Bimagic Graphs from Magic Graphs, Applied Mathematics, Volume 2, 393-396, 2011.
3. Ponnappan, C.Y., Nagaraj, C.T., and Prabakaran, G., Odd Vertex Magic Labeling, International Journal of Computer & Organization Trends – Volume 9 Number 1, Jun 2014.
4. Petr Kovar, Magic labelings of regular graphs, AKCE J. Graphs. Combin., Vol. 4, No.3,261-275, 2007.
5. Neelam Kumari1, Seema Mehra, E-super vertex magic labeling and V-super vertex labeling, International Journal of Scientific & Engineering Research, Volume 5, Issue 1, (January, 2014).
6. Neelam Kumari, and Seema Mehra, Some graphs with n-edge magic labeling, International Journal of Innovative Research in Science, Engineering and Technology, Vol. 2, Issue 10, (October 2013).

Citation :

A. Solairaju, S. Malathi, "Super Magic of Some Connected Graphs Pn * 2nP2 , Pn * 2nP3, Pn * 2nP4, and Pn * 2nP5," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 5, pp. 415-422, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P550