## Vertex magic total labelings of 2-regular graphs

- Feb. 9, 2018
- 2:30 p.m.
- LeConte 312

## Abstract

A \emph{vertex magic total (VMT) labeling} of a graph $G=(V,E)$ is a bijection from the set of vertices and edges to the set of integers defined by $\lambda:V\cup E \rightarrow \{1,2,\ldots,|V|+|E|\}$ so that for every $x\in V$, $w(x)=\lambda(x)+\sum _ {xy in E}\lambda(xy)=k$, for some integer $k$. A VMT labeling is said to be a \emph{super} VMT labeling if the vertices are labeled with the smallest possible integers, $1,2,\ldots, |V|$. In this paper we introduce a new method to expand some known VMT labelings of 2-regular graphs.