On metric dimension of generalized petersen graphs P(n, 3)

Muhammad Imran, A. Q. Baig, M. K. Shafiq, Loan Tomecu

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

In this paper we study the metric dimension of the generalized Petersen graphs P(n, 3) by giving a partial answer to an open problem raised in [8]: Is P(n,3) for n > 7 and 3 < m < L[n-1/2], a family of graphs with constant metric dimension? We prove that the generalized Petersen graphs P(n, 3) have metric dimension equal to 3 for n = 1(mod 6), n > 25, and to 4 for n = 0(mod 6), n > 24. For the remaining cases only 4 vertices appropriately chosen suffice to resolve all the vertices of P(n,3), thus implying that dim(P(n, 3)) < 4, except when n = 2(mod 6), when dim(P(n, 3)) < 5.

Original languageEnglish
Pages (from-to)113-130
Number of pages18
JournalArs Combinatoria
Volume117
Publication statusPublished - Oct 1 2014
Externally publishedYes

Keywords

  • Basis
  • Generalized petersen graph
  • Metric dimension
  • Resolving set

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'On metric dimension of generalized petersen graphs P(n, 3)'. Together they form a unique fingerprint.

Cite this