Bryan Freyberg

University of Minnesota, USA

On the Face-Magic Strength of Graphs

Bryan Freyberg, University of Minnesota Duluth, USA Let G be a graph with an embedding which induces a set of faces. A face-magic labeling of G is an assignment of consecutive integers to the vertices, edges, and faces of G so that for every n-sided face, the sum of its label and the labels of the vertices and edges surrounding it is equal to some fixed constant µ(n) for all n. If such a labeling exists, we call G a face-magic graph and the µ(n) are called its n-sided magic constants. Given a face-magic graph G, we ask: What is the spectrum for the n-sided magic constants? We explore this question for wheels, fans, the Cartesian product of two cycles, and the toroidal tiling of hexagons. Keywords: type (a, b, c) face-magic graph labeling, wheels, fans, Cartesian product of cycles, hexagonal tiling