Absolute Mean Graceful Labeling of Jewel Graph and Jelly Fish Graph

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2022 by IJMTT Journal
Volume-68 Issue-1
Year of Publication : 2022
Authors : P. Z. Akbari, V. J. Kaneria, N. A. Parmar
  10.14445/22315373/IJMTT-V68I1P510

MLA

MLA Style: P. Z. Akbari, V. J. Kaneria, N. A. Parmar. "Absolute Mean Graceful Labeling of Jewel Graph and Jelly Fish Graph" International Journal of Mathematics Trends and Technology 68.1 (2022):86-93. 

APA Style: P. Z. Akbari, V. J. Kaneria, N. A. Parmar(2022). Absolute Mean Graceful Labeling of Jewel Graph and Jelly Fish Graph. International Journal of Mathematics Trends and Technology, 68(1), 86-93.

Abstract
In this paper, we present absolute mean graceful labeling for some graphs. We have proved that jewel graph Jn, jewel graph without prime edge J*n, extended jewel graph E Jn, jelly fish graph Jm,n, jelly fish graph without prime edge J*m,n, extended jelly fish graph EJm,n are absolute mean graceful graphs.

Reference

[1] F. Harary, Graph theory, Addition Wesley, Massachusetts, (1972).
[2] A. Rosa, On certain valuation of the vertices of a graph, Theory of Graphs (Rome, July 1966), Gordon and Breach, N.Y. and Paris. (1967) 349-355.
[3] S. W. Golomb, How to number a graph, Graph Theory and Computing (R. C. Read. Ed.) Academic Press, New York, (1972) 23-37.
[4] J. A. Gallian, A dynamic survey of graph labeling, The Electronics Journal of Combinatorics, 22, #DS6 (2020).
[5] V. J. Kaneria, H. P. Chudasama and P. P. Andharia, Absolute mean graceful labeling in path union of various graphs, Math. J. Interdiscip. Sci. 7(1) (2018) 51-56.
[6] V. J. Kaneria and H. P. Chudasama, Absolute mean graceful labeling in various graphs, Int. J. Math. And Appl. 5(4) (2017) 723-726.
[7] V.J.Kaneria, H.M.Makadia and Meera Meghapara, Graceful labeling for grid related graphs, Int. J. of Mathematics and Soft Computing, 5(1)(2015), 111-117.
[8] V.J.Kaneria and H.M.Makadia, Graceful Labeling for Double Step Grid Graph, Int. J. of Mathematics and its Applications, 3(1)(2015), 33-38.
[9] F.Szabo, Linear Algebra: An Introduction Using Mathematica, Academic Press, (2000).
[10] I.Cahit, Cordial graphs: A weaker version of graceful and harmonious graphs, Ars Combin., 23(1987) 201-207.
[11] V.J.Kaneria and H.M.Makadia, Graceful labeling for swastik graph, Int. J. Math. Appl., 3(3-D)(2015) 25-29.
[12] B.D.Acharya and M. K. Gill, On the index of gracefulness of a graph and the gracefulness of two-dimensional square lattice graphs, Indian J. Math., 23(1981) 81-94.
[13] V.J.Kaneria, H.M.Makadia, M.M.Jariya and Meera Meghpara, Graceful labeling for complete bipartite graphs, Applied Math. Sci., 8(103) (2014) 5099-5104.
[14] V.Yagnanarayanan and P.Vaidhyanathan, Some intresting Applications of Graph Labeling, J. Math. Comput. Sci.,2(5)(2012) 1522-1531.
[15] S.K.Vaidya, N.A.Dani, K.K.Kanani and P.L.Vihol, Cordial and 3-equitable labeling for some star related graphs, International Mathematical Forum, 4(2009) 1543-1553.
[16] V.J.Kaneria, H.M.Makadia and R.V.Viradia, Various graph operations on semi smooth graceful graphs, International Journal of Math. and Soft Computing, 6(1)(2016) 57-79.
[17] V.J.Kaneria, Meera Meghpara and Maulik Khoda, Semi smooth graceful labeling and its application to produce α -labeling, J. Graph Labeling, 2(2) (2016) 153-160.
[18] S.K.Vaidya and N.B.Vyas, Some new results on mean labeling, Int. J. of Information Science and Computer Mathematics, 6(1-2) (2012) 19-29.
[19] V.J.Kaneria and M.M.Jariya, Semi smooth graceful graph and constraction of new graceful trees, Elixir Appl. Math., 76(2014) 28536-28538.
[20] V.J.Kaneria and M.M.Jariya, Smooth graceful graphs and its applications to constract graceful graphs, Int. J. Sci. and Res., 3(8)(2014) 909-912.
[21] S.K.Vaidya, S.Srivastav, V.J.Kaneria and G.V.Ghodasara, Cordial and 3-equitable labeling of star of a cycle, Mathematics Today, 24(2008), 54-64.
[22] V. J. Kaneria, Om Teraiya and Meera Meghpara, Double path union of α-graceful graph and its α-labeling, J. of Graph Labeling, 2(2)(2016) 107-114.
[23] V. J. Kaneria, Meera Meghpara and H. M. Makadia, Graceful labeling for open star of graphs, Inter. J. of Mathematics and Statistics Invention, 2(9)(2014) 19-23.
[24] V.J.Kaneria and S.K.Vaidya, Index of cordiality for complete graphs and cycle, IJAMC, 2(4)(2010) 38-46.
[25] V.J.Kaneria, Hardik Makadia and Meera Meghpara, Cordiality of star of the complete graph and a cycle graph (n . Kn), J. of Math. Research, 6(4)(2014) 18-28.

Keywords : Labeling, Graceful labeling, Absolute mean graceful labeling.