Distance magic labeling in complete 4-partite graphs

2014/10/25 by Daniel Kotlar, Kotlar, Dani
Computer Science · Engineering · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1410.6916

openalex publication_date 2014/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a complete k-partite simple undirected graph with parts of sizes p₁≤ p₂...≤ p_k. Let P_j=∑_i=1^jp_i for j=1,...,k. It is conjectured that G has distance magic labeling if and only if ∑_i=1^P_j (n-i+1)≥ jn+1\choose2/k for all j=1,...,k. The conjecture is proved for k=4, extending earlier results for k=2,3.

Citations

• A Dynamic Survey of Graph Labeling

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