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 language | English |
---|---|
Pages (from-to) | 113-130 |
Number of pages | 18 |
Journal | Ars Combinatoria |
Volume | 117 |
Publication status | Published - Oct 1 2014 |
Externally published | Yes |
Keywords
- Basis
- Generalized petersen graph
- Metric dimension
- Resolving set
ASJC Scopus subject areas
- General Mathematics