2013/12/30 by Rinovia Simanjuntak, Simanjuntak, Rinovia, Mona Elviyenti +7
Computer Science · #05C78 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.1312.7633
openalex publication_date 2013/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an arbitrary set of distances D⊆ \0,1, …, d\, a graph G is said to be D-distance magic if there exists a bijection f:V→ \1,2, … , v\ and a constant \sf k such that for any vertex x, ∑y∈ ND(x) f(y) =\sf k, where ND(x) = \y ∈ V| d(x,y) ∈ D\. In this paper we study some necessary or sufficient conditions for the existence of D-distance magic graphs, some of which are generalization of conditions for the existence of \1\-distance magic graphs. More specifically, we study D-distance magic labelings for cycles and D-distance magic graphs for D⊆\0,1,2\.