On Regular Distance Magic Graphs of Odd Order
Result description
Let G = (V, E) be a graph with n vertices. A bijection f : V -> {1, 2, . . ., n} is called a distance magic labeling of G if there exists an integer k such that the sum of neighbours weights of v is k for all v in V, where N(v) is the set of all vertices adjacent to v. Any graph which admits a distance magic labeling is a distance magic graph. The existence of regular distance magic graphs of even order was solved completely in a paper by Fronček, Kovář, and Kovářová. In two recent papers, the existence of 4-regular and of (n-3)-regular distance magic graphs of odd order was also settled completely. In this paper, we provide a similar classification of all feasible odd orders of r-regular distance magic graphs when r = 6, 8, 10, 12. Even though some nonexistence proofs for small orders are done by brute force enumeration, all the existence proofs are constructive. (C) 2023 Charles Babbage Research Centre. All rights reserved.
Keywords
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/61989100:27740/23:10254518
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
On Regular Distance Magic Graphs of Odd Order
Original language description
Let G = (V, E) be a graph with n vertices. A bijection f : V -> {1, 2, . . ., n} is called a distance magic labeling of G if there exists an integer k such that the sum of neighbours weights of v is k for all v in V, where N(v) is the set of all vertices adjacent to v. Any graph which admits a distance magic labeling is a distance magic graph. The existence of regular distance magic graphs of even order was solved completely in a paper by Fronček, Kovář, and Kovářová. In two recent papers, the existence of 4-regular and of (n-3)-regular distance magic graphs of odd order was also settled completely. In this paper, we provide a similar classification of all feasible odd orders of r-regular distance magic graphs when r = 6, 8, 10, 12. Even though some nonexistence proofs for small orders are done by brute force enumeration, all the existence proofs are constructive. (C) 2023 Charles Babbage Research Centre. All rights reserved.
Czech name
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Czech description
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Classification
Type
JSC - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
The Journal of Combinatorial Mathematics and Combinatorial Computing
ISSN
0835-3026
e-ISSN
2817-576X
Volume of the periodical
117
Issue of the periodical within the volume
Neuveden
Country of publishing house
CA - CANADA
Number of pages
10
Pages from-to
55-64
UT code for WoS article
—
EID of the result in the Scopus database
2-s2.0-85184135530
Basic information
Result type
JSC - Article in a specialist periodical, which is included in the SCOPUS database
OECD FORD
Applied mathematics
Year of implementation
2023