Odd Vertex-In Magic Total Labeling of Some 2-Regular Digraphs

# M. Sindhu1 and S. Chandra Kumar2

1Department of Mathematics, Excel Engineering college (Autonomous), Komarapalayam, Namakkal, Tamilnadu, India.
2Department of Mathematics, Scott Christian College (Autonomous), Nagercoil, Tamilnadu, India.

Abstract: Let D be a directed graph with p vertices and q arcs. A vertex in-magic total labeling (VIMTL) of a graph D is a bijection $f:V\left(D\right)\cup A\left(D\right)\to \left\{1,2,\dots p+q\right\}$ with the property that for every $v\in V(D)$, $f\left(v\right)+\sum\limits_{u\in I(v)}{f(\left(v,u\right))=M}$, for some constant M. Such labeling is `Odd' if $f\left(V(D)\right)=\left\{1,3,\dots ,2p-1\right\}$. In this paper, we explore the Odd Vertex In-magic total labeling (OVIMTL) of some 2-regular directed graphs.
Keywords: Digraphs, vertex in-magic labeling, Odd Vertex in-magic total labeling.

Cite this article as: M. Sindhu and S. Chandra Kumar, Odd Vertex-In Magic Total Labeling of Some 2-Regular Digraphs, Int. J. Math. And Appl., vol. 10, no. 1, 2022, pp. 59-65.

References
1. J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Elsevier, North Holland, New York, (1986).
2. J. A. Gallian, A dynamic survey of graph labeling electronic, J. Combinatorics, 5(2002), \#D56.
3. J. A. MacDougall, M. Miller and W. D. Wallis, Vertex magic total labeling of graphs, Util. Math., 61(2002), 3-21.
4. J. A. MacDougall, M. Miller and K. A. Sugeng, Super vertex-magic total labelings of graphs, in: Proceedings of the 15th Australian Workshop on Combinatorial Algorithms, (2004), 222-229.
5. J. Sedlacek, Problem 27, in Theory of Graphs and its Applications, Proc. Symposium Smolenice, (1963), 163-167.
6. G. S. Bloom, A. Marr and W. D. Wallis, Magic Digraphs, J. Combin. Math. Combin. Comput., 65(2008), 205-212.
7. G. Durga Devi, M. Durga and G. Marimuthu, V-Super Vertex Out-Magic Total Labelings of Digraphs, Commun. Korean Math. Soc., 32(2)(2017), 435-445.
8. C. T. Nagaraj, C. Y. Ponnappan and G. Prabakaran, Odd vertex magic total labeling of some graphs, International Journal of Pure and Applied Mathematics, 118(10)(2018), 97-109.
9. C. T.Nagaraj, C. Y. Ponnappan and G. Prabakaran, Odd vertex magic total labeling of some 2-regular graphs, International Journal of Mathematics Trends and Technology, 54(1)(2018), 34-41.

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