Uniquely identifying the edges of a graph : the edge metric dimension
Kelenc, Aleksander ; Tratnik, Niko ; Yero, Ismael G.
Let ▫$G = (V, E)$▫ be a connected graph, let ▫$v \in V$▫ be a vertex and let ▫$e = u w \in E$▫ be an edge. The distance between the vertex ▫$v$▫ and the edge ▫$e$▫ is given by ▫$d_G(e, v) = \min ...\{d_G(u, v), d_G(w, v) \}$▫. A vertex ▫$w \in V$▫ distinguishes two edges ▫$e_1, e_2 \in E$▫ if ▫$d_G(w, e_1) \ne d_G(w, e_2)$▫. A set $S$ of vertices in a connected graph ▫$G$▫ is an edge metric generator for ▫$G$▫ if every two edges of ▫$G$▫ are distinguished by some vertex of ▫$S$▫. The smallest cardinality of an edge metric generator for ▫$G$▫ is called the edge metric dimension and is denoted by ▫$edim(G)$▫. In this paper, we introduce the concept of edge metric dimension and initiate the study of its mathematical properties. We make a comparison between the edge metric dimension and the standard metric dimension of graphs while presenting some realization results concerning the edge metric dimension and the standard metric dimension of graphs. We prove that computing the edge metric dimension of connected graphs is NP-hard and give some approximation results. Moreover, we present some bounds and closed formulae for the edge metric dimension of several classes of graphs.
It was not necessary to add the material to the shelf.
Bibliographic material was successfully added on shelf.
Adding bibliographical material on shelf was not successful.
Material is already on the shelf.
Permalink
URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year
Impact factor
Edition
Category
Classification
JCR
SNIP
JCR
SNIP
JCR
SNIP
JCR
SNIP
Select the library membership card:
DRS,
in which the journal is indexed
Database name
Field
Year
Links to authors' personal bibliographies
Links to information on researchers in the SICRIS system
Subject headings in COBISS General List of Subject Headings
Select pickup location
The material from the parent unit is free. If the material is delivered to the pickup location from another unit, the library may charge you for this service.
PDF
Miklošičeva knjižnica - FPNM bo od 17. 6. 2024 do 30. 9. 2024 odprta vsak dan od ponedljka do petka od 8.00 do 14.00.
Srečno.
Kolektiv Miklošičeve knjižnice - FPNM