1. D-Magic Oriented Graphs
- Author
-
Alison Marr and Rinovia Simanjuntak
- Subjects
oriented graphs ,digraph labeling ,distance magic labeling ,D-magic labeling ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Astrophysics::High Energy Astrophysical Phenomena ,Magic (programming) ,Construct (python library) ,Graph ,Vertex (geometry) ,Combinatorics ,Set (abstract data type) ,Magic constant ,Multipartite ,Chemistry (miscellaneous) ,Homogeneous space ,Computer Science (miscellaneous) ,Physics::Atomic and Molecular Clusters ,QA1-939 ,Mathematics ,MathematicsofComputing_DISCRETEMATHEMATICS - Abstract
In this paper, we define D-magic labelings for oriented graphs where D is a distance set. In particular, we label the vertices of the graph with distinct integers {1,2,…,|V(G)|} in such a way that the sum of all the vertex labels that are a distance in D away from a given vertex is the same across all vertices. We give some results related to the magic constant, construct a few infinite families of D-magic graphs, and examine trees, cycles, and multipartite graphs. This definition grew out of the definition of D-magic (undirected) graphs. This paper explores some of the symmetries we see between the undirected and directed version of D-magic labelings.
- Published
- 2021