Some Absolute Mean Graceful Graphs in the Context of
Barycentric Subdivision

P. Z. Akbari; V. J. Kaneria; N. A. Parmar

doi:https://doi.org/10.14445/22315373/IJMTT-V68I5P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 5 | Year 2022 | Article Id. IJMTT-V68I5P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I5P509

Some Absolute Mean Graceful Graphs in the Context of Barycentric Subdivision

P. Z. Akbari, V. J. Kaneria, N. A. Parmar

Received	Revised	Accepted	Published
23 May 2022	18 May 2022	29 May 2022	09 Jun 2022

Abstract

In this paper, we present absolute mean graceful labeling for some graphs in context of barycentric subdivision of graph. We have proved that barycentric subdivision of wheel 𝑊𝑛, complete bipartite graph 𝐾𝑚,𝑛, helm 𝐻𝑛, sunlet graph 𝑆𝑛, jelly fish graph 𝐽𝑛,𝑛, alternate quadrilateral snake 𝐴𝑄𝑛 are absolute mean graceful graphs.

Keywords

Labeling, Graceful Labeling, Absolute Mean Graceful Labeling.

References

[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, P. Z. Akbari and N. A. Parmar, Some Absolute Mean Graceful Graphs, Int. J. Math. Trends and Tech. 68(1)(2022)86-93.
[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.

Citation :

P. Z. Akbari, V. J. Kaneria, N. A. Parmar, "Some Absolute Mean Graceful Graphs in the Context of Barycentric Subdivision," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 5, pp. 51-60, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I5P509