The Metric Dimension of Some Generalized Petersen Graphs
Joint Authors
Liu, Jia-Bao
Shao, Zehui
Sheikholeslami, S. M.
Wu, Pu
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-08-01
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
The distance d(u,v) between two distinct vertices u and v in a graph G is the length of a shortest (u,v)-path in G.
For an ordered subset W={w1,w2,…,wk} of vertices and a vertex v in G, the code of v with respect to W is the ordered k-tuple cW(v)=(d(v,w1),d(v,w2),…,d(v,wk)).
The set W is a resolving set for G if every two vertices of G have distinct codes.
The metric dimension of G is the minimum cardinality of a resolving set of G.
In this paper, we first extend the results of the metric dimension of P(n,3) and P(n,4) and study bounds on the metric dimension of the families of the generalized Petersen graphs P(2k,k) and P(3k,k).
The obtained results mean that these families of graphs have constant metric dimension.
American Psychological Association (APA)
Shao, Zehui& Sheikholeslami, S. M.& Wu, Pu& Liu, Jia-Bao. 2018. The Metric Dimension of Some Generalized Petersen Graphs. Discrete Dynamics in Nature and Society،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1152593
Modern Language Association (MLA)
Shao, Zehui…[et al.]. The Metric Dimension of Some Generalized Petersen Graphs. Discrete Dynamics in Nature and Society No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1152593
American Medical Association (AMA)
Shao, Zehui& Sheikholeslami, S. M.& Wu, Pu& Liu, Jia-Bao. The Metric Dimension of Some Generalized Petersen Graphs. Discrete Dynamics in Nature and Society. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1152593
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1152593