On Regular Distance Magic Graphs of Odd Order

Kód výsledku v IS VaVaI

RIV/61989100:27240/23:10254518 - isvavai.cz

Nalezeny alternativní kódy

RIV/61989100:27740/23:10254518

Výsledek na webu

https://combinatorialpress.com/jcmcc-articles/volume-117/on-regular-distance-magic-graphs-of-odd-order/

DOI - Digital Object Identifier

10.61091/jcmcc117-06

Jazyk výsledku

angličtina

Název v původním jazyce

On Regular Distance Magic Graphs of Odd Order

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On Regular Distance Magic Graphs of Odd Order

Popis výsledku anglicky

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.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

The Journal of Combinatorial Mathematics and Combinatorial Computing

ISSN

0835-3026

e-ISSN

2817-576X

Svazek periodika

117

Číslo periodika v rámci svazku

Neuveden

Stát vydavatele periodika

CA - Kanada

Počet stran výsledku

10

Strana od-do

55-64

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85184135530