Distance magic labelings

Abstract

Title: Distance Magic Labelings Author: Hayden Pfeiffer Department: Dept. of Theoretical Computer Science and Mathematical Logic Supervisor: doc. Mgr. Petr Gregor, Ph.D., KTIML, MFF UK Abstract: A distance magic labeling of a graph G is a bijection f : V (G) → {1, 2, . . . , |V (G)|} such that the sum of labels on the neighbourhood of each vertex is constant. A framework based on linear algebra has been developed using the notion of neighbour balance to determine whether there exists a distance magic labeling for a hypercube with dimension n. In this thesis, we extend this framework to all Cayley graphs on Zn 2 . We use this framework to reprove some known results from recent literature. We also use this framework to introduce the notion of component-wise distance magic labelings on Cayley graphs of Zn 2 . Keywords: distance magic labeling, Cayley graph, hypercube, neighbour balance iii