The edge partition dimension of graphs | [Discrete Mathematics Letters • 2023]

Author(s):

1. Dorota Kuziak: Departamento de Estad ́ıstica e Investigacio ́n Operativa, Universidad de C a ́diz,Algeciras,Spain

2. Elizabeth Maritz: Department of Mathematics and Applied Mathematics, University of the Free State,Bloemfontein,South Africa

3. Tomas Vetrik: Department of Mathematics and Applied Mathematics, University of the Free State,Bloemfontein,South Africa

4. Ismael G. Yero: Departamento de Matem a ́ticas, Universidad de C a ́diz,Algeciras,Spain

Abstract:

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.

Page(s): 34-39

DOI: 10.47443/dml.2023.010

Published: Journal: Discrete Mathematics Letters, Volume: 12, Issue: 0, Year: 2023

Keywords:

partition dimension , edge resolving partition , edge partition dimension , edge metric dimension

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