Fault-Tolerant Metric Dimension of Generalized Wheels and Convex Polytopes
Joint Authors
Ahmad, Ashfaq
Liu, Jia-Bao
Ali, Imtiaz
Qureshi, Muhammad Imran
Zheng, Zhi-Bo
Hussain, Zaffar
Munir, Mobeen
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-04
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
For a graph G, an ordered set S⊆VG is called the resolving set of G, if the vector of distances to the vertices in S is distinct for every v∈VG.
The minimum cardinality of S is termed as the metric dimension of G.
S is called a fault-tolerant resolving set (FTRS) for G, if S\v is still the resolving set ∀v∈VG.
The minimum cardinality of such a set is the fault-tolerant metric dimension (FTMD) of G.
Due to enormous application in science such as mathematics and computer, the notion of the resolving set is being widely studied.
In the present article, we focus on determining the FTMD of a generalized wheel graph.
Moreover, a formula is developed for FTMD of a wheel and generalized wheels.
Recently, some bounds of the FTMD of some of the convex polytopes have been computed, but here we come up with the exact values of the FTMD of two families of convex polytopes denoted as Dk for k≥4 and Qk for k≥6.
We prove that these families of convex polytopes have constant FTMD.
This brings us to pose a natural open problem about the existence of a polytope having nonconstant FTMD.
American Psychological Association (APA)
Zheng, Zhi-Bo& Ahmad, Ashfaq& Hussain, Zaffar& Munir, Mobeen& Qureshi, Muhammad Imran& Ali, Imtiaz…[et al.]. 2020. Fault-Tolerant Metric Dimension of Generalized Wheels and Convex Polytopes. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-8.
https://search.emarefa.net/detail/BIM-1193058
Modern Language Association (MLA)
Zheng, Zhi-Bo…[et al.]. Fault-Tolerant Metric Dimension of Generalized Wheels and Convex Polytopes. Mathematical Problems in Engineering No. 2020 (2020), pp.1-8.
https://search.emarefa.net/detail/BIM-1193058
American Medical Association (AMA)
Zheng, Zhi-Bo& Ahmad, Ashfaq& Hussain, Zaffar& Munir, Mobeen& Qureshi, Muhammad Imran& Ali, Imtiaz…[et al.]. Fault-Tolerant Metric Dimension of Generalized Wheels and Convex Polytopes. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-8.
https://search.emarefa.net/detail/BIM-1193058
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193058