New Constructions of A-magic Graphs Using Labeling Matrices

A simple graph \( G(V, E) \) is called \( A \)-magic if there is a labeling \( f: E \to A^* \), where \( A \) is an Abelian group and \( A^* = A – \{0\} \), such that the induced vertex labeling \( f^*: V \to A \), defined as \( f^*(v) = \sum_{u \in N(v)} f(uv) = k \), 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.