Multiple Magic Graphs

Abstract

Let $G$ be a graph of order $n$ and size $m$. A vertex magic total labeling is an assignment of the integers $1, 2, 3, ... ,m+n$ to the vertices and the edges of $G$, so that at each vertex , the vertex label and the labels on the edges incident at that vertex, add to a fixed constant called the magic constant of $G$. Such a labeling is a-vertex multiple magic if the set of the labels of the vertices is $\{a, 2a, ..., na\}$ and is b-edge multiple magic if the set of labels of the edges is $\{b, 2b, ..., mb\}$. This article, presents properties of $a-$ vertex multiple magic graphs and $b-$ edge multiple magic graphs.