The Edge Partition Dimension of Graphs

  1. Dorota Kuziak 3
  2. Elizabeth Maritz 1
  3. Tomas Vetrìk 1
  4. Ismael G. Yero 2
  1. 1 Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa
  2. 2 Departamento de Matematicas, Universidad de C ´ adiz, Algeciras, Spain
  3. 3 Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Algeciras, Spain
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Revista:
Discrete Mathematics Letters

ISSN: 2664-2557

Año de publicación: 2023

Volumen: 12

Páginas: 34-39

Tipo: Artículo

DOI: 10.47443/DML.2023.010 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Discrete Mathematics Letters

Resumen

The edge metric dimension was introduced in 2018 and since then, it has been extensively studied. In this paper, we present a different way to obtain resolving structures in graphs in order to gain more insight into the study of edge resolving sets and resolving partitions. We define the edge partition dimension of a connected graph and bound it for graphs of given order and for graphs with given maximum degree. We obtain exact values of the edge partition dimension for multipartite graphs. Some relations between the edge partition dimension and partition dimension/edge metric dimension are also presented. Moreover, several open problems for further research are stated.