Spectra of graphs and closed distance magic labelings

Marcin Anholcer , Sylwia Cichacz , Iztok Peterin

Abstract

Let G = (V, E) be a graph of order n. A closed distance magic labeling of G is a bijection ℓ: V(G) → {1, . . . , n}for which there exists a positive integer k such that x∈N[v] ℓ(x) = k for all v ∈ V, where N[v] is the closed neighborhood of v. 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.
Author Marcin Anholcer (WIiGE / KBO)
Marcin Anholcer,,
- Department of Operations Research
, Sylwia Cichacz - AGH University of Science and Technology (AGH), MNiSW [80]
Sylwia Cichacz,,
-
, Iztok Peterin - University of Maribor, Slovenia
Iztok Peterin,,
-
Journal seriesDiscrete Mathematics, ISSN 0012-365X, (A 25 pkt)
Issue year2016
Vol339
No7
Pages1915-1923
Publication size in sheets0.5
Keywords in EnglishClosed distance magic graphs, Graph spectrum, Strong product of graphs
ASJC Classification2607 Discrete Mathematics and Combinatorics; 2614 Theoretical Computer Science
DOIDOI:10.1016/j.disc.2015.12.025
URL https://www.sciencedirect.com/science/article/pii/S0012365X15004665
Languageen angielski
Score (nominal)25
Score sourcejournalList
ScoreMinisterial score = 25.0, 10-01-2020, ArticleFromJournal
Ministerial score (2013-2016) = 25.0, 10-01-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 1.028; WoS Impact Factor: 2016 = 0.639 (2) - 2016=0.698 (5)
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