Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646711 | Discrete Mathematics | 2016 | 9 Pages |
Abstract
Let G=(V,E)G=(V,E) be a graph of order nn. A closed distance magic labeling of GG is a bijection ℓ:V(G)→{1,…,n}ℓ:V(G)→{1,…,n} for which there exists a positive integer kk such that ∑x∈N[v]ℓ(x)=k∑x∈N[v]ℓ(x)=k for all v∈Vv∈V, where N[v]N[v] is the closed neighborhood of vv. We consider the closed distance magic graphs in the algebraic context. In particular we analyze the relations between the closed distance magic labelings and the spectra of graphs. These results are then applied to the strong product of graphs with complete graph or cycle and to the circulant graphs. We end with a number theoretic problem whose solution results in another family of closed distance magic graphs somewhat related to the strong product.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Marcin Anholcer, Sylwia Cichacz, Iztok Peterin,