2019/03/11 by Rinovia Simanjuntak, Simanjuntak, Rinovia, Palton Anuwiksa +1
Computer Science · Mathematics · #05C12 #05C78 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1903.04459
openalex publication_date 2019/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a set of distances D, a graph G on n vertices is said to be D-magic if there exists a bijection f:V→ \1,2, … , n\ and a constant k such that for any vertex x, ∑y∈ ND(x) f(y) = k, where ND(x)=\y|d(x,y)=i, i∈ D\ is the D-neighbourhood set of x. In this paper we utilize spectra of graphs to characterize strongly regular graphs which are D-magic, for all possible distance sets D. In addition, we provide necessary conditions for distance regular graphs of diameter 3 to be \1\-magic.