Constructing Distance Magic Graphs from Regular Graphs

Abstract

A graph $G$ with $k$ vertices is distance magic if the vertices can be labeled with numbers $1,2,\dots ,k$ 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.