New Constructions of A-magic Graphs Using Labeling Matrices

Abstract

A simple graph $G(V,E)$ is called $A$-magic if there is a labeling $f:E\to A^{\ast }$, where $A$ is an Abelian group and $A^{\ast }=A–\{0\}$, such that the induced vertex labeling $f^{\ast }:V\to A$, defined as $f^{\ast }(v)=\sum _{u\in N(v)}f(uv)=k$, for every $v\in V$, is a constant in $A$. In this paper, we show constructions of new classes of $A$-magic graphs from known $A$-magic graphs using labeling matrices.