Speaker:   Dalibor Froncek
  Department of Mathematics and Statistics
  University of Minnesota Duluth

Title:  Magic type labelings of cycle products

Abstract: A Cartesian product of two cycles Cm and Cn can be seen as a toroidal m x n grid with mn vertices of degree four and 2mn edges. We can bijectively label edges, vertices, or both by consecutive positive integers 1,2,…,s or by elements of an Abelian group of order s (where s is the number of labeled elements) and define the weight of an element (that is, an edge or a vertex) as the sum of labels of the adjacent and/or incident elements. When the weights of all elements in question are equal, we call the labeling magic (of some kind). When the weights are all different, the labeling is called antimagic. I will present some old and new results on various kinds of magic labelings of cycle products and pose several open questions. The results are based on collaboration with several co-authors, including Tereza Kovářová, Petr Kovář, Jack McKeown, James McKeown, Michael McKeown, and Jiangyi Qiu.