The integer-magic spectra and null sets of the cartesian product of trees
Wai Chee Shiu, Richard M. Low · HKBU Institutional Repository (Hong Kong Baptist University) · 2018
Let A be a non-trivial, finitely-generated abelian group and A * = A\{0}.A graph is A-magic if there exists an edge labeling f using elements of A * which induces a constant vertex labeling of the graph.Such a labeling f is called an A-magic labeling and the constant value of the induced vertex labeling is called the A-magic value.The integer-magic spectrum of a graph G is the setwhere N is the set of natural numbers.The null set of G is the set of integers k ∈ N such that G has a Z k -magic labeling with magic value 0. In this paper, we determine the integer-magic spectra and null sets of the Cartesian product of two trees.