Edge Metric Dimension of Some Generalized Petersen Graphs

The edge metric dimension problem was recently introduced, which initiated the study of its mathematical properties. The theoretical properties of the edge metric representations and the edge metric dimension of generalized Petersen graphs GP ( n ,  k ) are studied in this paper. We prove the exact...

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Vydané v:Resultate der Mathematik Ročník 74; číslo 4
Hlavní autori: Filipović, Vladimir, Kartelj, Aleksandar, Kratica, Jozef
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.12.2019
Predmet:
Mathematics
Mathematics and Statistics
05C12
generalized Petersen graphs
90C35
Edge metric dimension
68R10
discrete mathematics
ISSN:1422-6383, 1420-9012
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Popis
Shrnutí:The edge metric dimension problem was recently introduced, which initiated the study of its mathematical properties. The theoretical properties of the edge metric representations and the edge metric dimension of generalized Petersen graphs GP ( n ,  k ) are studied in this paper. We prove the exact formulae for GP ( n , 1) and GP ( n , 2), while for other values of k a lower bound is stated.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-019-1105-9