On the Edge Resolvability of Double Generalized Petersen Graphs

Tanveer Iqbal, Muhammad Rafiq, Muhammad Naeem Azhar, Muhammad Salman, Imran Khalid and Ali Ahmad

Journal of Mathematics, 2022, vol. 2022, 1-14

Abstract: For a connected graph G=VG,EG, let v∈VG be a vertex and e=uw ∈EG be an edge. The distance between the vertex v and the edge e is given by dGe,v=mindGu,v,dGw,v. A vertex w∈VG distinguishes two edges e1,e2∈EG if dGw,e1≠dGw,e2. A well-known graph invariant related to resolvability of graph edges, namely, the edge resolving set, is studied for a family of 3-regular graphs. 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 βeG. As a main result, we investigate the minimum number of vertices which works as the edge metric generator of double generalized Petersen graphs, DGPn,1. We have proved that βeDGPn,1=4 when n≡0,1,3mod4 and βeDGPn,1=3 when n≡2mod4.

Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2022/6490698.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2022/6490698.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6490698

DOI: 10.1155/2022/6490698

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().