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

# M. Sindhu^{1} and S. Chandra Kumar^{2}

^{1}Department of Mathematics, Excel Engineering college (Autonomous), Komarapalayam, Namakkal, Tamilnadu, India.

^{2}Department 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.

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