NEW RESULTS ON SUPER EDGE
MAGIC DEFICIENCY OF KITE GRAPHS
Muhammad Imran1,2, Saima Sami Khan3, Sarfraz Ahmad3,
Muhammad Faisal Nadeem3, Muhammad Kamran Siddiqui3
1Department of Mathematical Sciences
United Arab Emirates University, UAE
2Department of Mathematics
School of Natural Sciences
National University of Sciences and Technology, PAKISTAN
3Department of Mathematics
COMSATS University Islamabad
Lahore Campus, 54000, PAKISTAN

Abstract

An edge magic labeling of a graph $G$ is a bijection $\lambda:V(G)\cup E(G)\rightarrow \{1, 2, \dots ,\vert V(G)\vert+\vert E(G)\vert \}$ such that $\lambda(u)+\lambda(uv)+\lambda(v)$ is constant, for every edge $uv\in E(G).$ The concept of edge magic deficiency was introduce by Kotzig and Rosa’s. Motivated by this concept Figueroa-Centeno, Ichishima and Muntaner-Batle defined a similar concept for super edge magic total labelings.

The super edge magic deficiency of a graph $G,$ which is denoted by $\mu_s(G),$ is the minimum nonnegative integer $n$ such that $G\cup nK_1,$ has a super edge magic total labeling or it is equal to $+\infty$ if there exists no such $n.$ In this paper, we study the super edge magic deficiency of kite graphs.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 6
Year: 2019

DOI: 10.12732/ijam.v32i6.6

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References

  1. [1] A. Ahmad, I. Javaid and M. F. Nadeem, Further results on super edge magic deficiency of unicyclic graphs, Ars Combin., 99 (2011), 129-138.
  2. [2] A. Ahmad and F. A. Muntaner-Batle, On Super Edge-Magic Deficiency of Unicyclic Graphs, Preprint.
  3. [3] A. Ahmad, A. Q. Baig and M. Imran, On super edge-magicness of graphs, Utilitas Math., 89 (2012), 373-380.
  4. [4] A. Ahmad, M.K. Siddiqui, M. F. Nadeem and M. Imran, On super edge magic deficiency of kite graps, Ars Combin., 107 (2012), 201-208.
  5. [5] A. Q. Baig, Super Edge-Mmagic Deficiency of Forests, PhD Thesis (2011).
  6. [6] A. Q. Baig, E. T. Baskoro and A. Semaničová-Feňovčı́ková, On the super edgemagic deficiency of a star forest, Ars Combin., 106 (2012), 115-125.
  7. [7] A. Q. Baig, A. Ahmad, E. T. Baskoro and R. Simanjuntak, On the super edgemagic deficiency of forests, Utilitas Math., 89 (2011), 147-159.
  8. [8] R. M. Figueroa, R. Ichishima and F. A. Muntaner-Batle, The place of super edge-magic labeling among other classes of labeling, Discrete Math., 231 (2001), 153-168.
  9. [9] R. M. Figueroa-Centeno, R. Ichishima and F. A. Muntaner-Batle, On the super edge magic deficiency of graphs, Electron. Notes Discrete Math., 11, (2002), 98-409.
  10. [10] R. M. Figueroa-Centeno, R. Ichishima, F. A. Muntaner-Batle, On the super Edge-Magic Deficiency of Graphs, Ars Combin., 78 (2006), 33-46.
  11. [11] J. A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin.; http://www.combinatorics.org/surveys/ds6.pdf (2010).
  12. [12] M. Hussain, E. T. Baskoro, K. Ali, On super antimagic total labeling of Harary graph, Ars Combin., 92 (2016), 120-130.
  13. [13] M. Hussain, E. T. Baskoro, Slamin, On super edge-magic total labeling of banana trees, Utilitas Math., 79 (2009), 243-251.
  14. [14] S.-R. Kim and J. Y. Park, On super edge-magic graphs, Ars Combin., 81 (2006), 113-127.
  15. [15] A. Kotzig and A. Rosa, Magic valuaton of finite graphs, Canad. Math. Bull. 13(4) (1970), 451-461.
  16. [16] A.A.G. Ngurah, R. Simanjuntak, and E.T. Baskoro, On the super edgemagic deficiencies of graphs, Australas. J. Combin., 40 (2008), 3-14.
  17. [17] J. Y. Park, J. H. Choi and J-H. Bae, On super edge-magic labeling of some graphs, Bull. Korean Math. Soc., 45 (2008), 11-21.
  18. [18] W. D. Wallis, Magic Graphs, Birkhäuser, Boston, 2001.
  19. [19] W. D. Wallis, E. T. Baskoro, M. Miller, and Slamin, Edge-magic total labelings, Australas. J. Combin., 22 (2000), 177-190.