Contents

Constructing Distance Magic Graphs from Regular Graphs

Dalibor Froncek1, Petr Kovank2, Tereza Kovarova2
1University of Minnesota Duluth,
2Technical University of Ostrava

Abstract

A graph \( G \) with \( k \) vertices is distance magic if the vertices can be labeled with numbers \( 1, 2, \ldots, k \) so that the sum of labels of the neighbors of each vertex is equal to the same constant \( \mu_0 \). We present a construction of distance magic graphs arising from arbitrary regular graphs based on an application of magic rectangles. We also solve a problem posed by Shafig, Ali, and Simanjuntak.

Keywords: Magic type labeling, distance magic labeling, 1-vertex-magic vertex labeling, magic rectangles.