On Distance Magic Harary Graphs

TL;DR

This paper introduces methods to construct larger distance magic and antimagic graphs using Harary graphs and solves the existence problem of distance magicness in certain graph products involving non-regular graphs.

Contribution

It develops two techniques for constructing larger distance magic and antimagic graphs and provides a solution for the existence of distance magicness in specific graph products.

Findings

Constructed larger distance magic graphs from Harary graphs.

Solved the existence problem for distance magicness in G[C4] and G×C4.

Established conditions for non-regular distance magic graphs.

Abstract

This paper establishes two techniques to construct larger distance magic and (a, d)-distance antimagic graphs using Harary graphs and provides a solution to the existence of distance magicness of legicographic product and direct product of G with C4, for every non-regular distance magic graph G with maximum degree |V(G)|-1.