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

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.