Computing the metric dimension of convex polytopes generated by wheel related graphs

M. Imran; H. M.A. Siddiqui

doi:10.1007/s10474-016-0606-1

Computing the metric dimension of convex polytopes generated by wheel related graphs

M. Imran, H. M.A. Siddiqui

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

An ordered set W= { w₁,.. , w_k} ⫅ V(G) of vertices of G is called a resolving set or locating set for G if every vertex is uniquely determined by its vector of distances to the vertices in W. A resolving set of minimum cardinality is called a metric basis for G and this cardinality is the metric dimension or location number of G, denoted by β(G). The metric dimension of certain wheel related graphs has been studied recently in [22]. In this paper, we extend this study to infinite classes of convex polytopes generated by wheel related graphs. We prove that these infinite classes of convex polytopes generated by wheel related graphs have unbounded metric dimension. It is natural to ask for the characterization of graphs with unbounded metric dimension.

Original language	English
Pages (from-to)	10-30
Number of pages	21
Journal	Acta Mathematica Hungarica
Volume	149
Issue number	1
DOIs	https://doi.org/10.1007/s10474-016-0606-1
Publication status	Published - Jun 2016
Externally published	Yes

Keywords

basis
convex polytope
metric dimension
resolving set
wheel related graph

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s10474-016-0606-1

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title = "Computing the metric dimension of convex polytopes generated by wheel related graphs",

abstract = "An ordered set W= { w1,.. , wk} ⫅ V(G) of vertices of G is called a resolving set or locating set for G if every vertex is uniquely determined by its vector of distances to the vertices in W. A resolving set of minimum cardinality is called a metric basis for G and this cardinality is the metric dimension or location number of G, denoted by β(G). The metric dimension of certain wheel related graphs has been studied recently in [22]. In this paper, we extend this study to infinite classes of convex polytopes generated by wheel related graphs. We prove that these infinite classes of convex polytopes generated by wheel related graphs have unbounded metric dimension. It is natural to ask for the characterization of graphs with unbounded metric dimension.",

keywords = "basis, convex polytope, metric dimension, resolving set, wheel related graph",

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AU - Siddiqui, H. M.A.

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N2 - An ordered set W= { w1,.. , wk} ⫅ V(G) of vertices of G is called a resolving set or locating set for G if every vertex is uniquely determined by its vector of distances to the vertices in W. A resolving set of minimum cardinality is called a metric basis for G and this cardinality is the metric dimension or location number of G, denoted by β(G). The metric dimension of certain wheel related graphs has been studied recently in [22]. In this paper, we extend this study to infinite classes of convex polytopes generated by wheel related graphs. We prove that these infinite classes of convex polytopes generated by wheel related graphs have unbounded metric dimension. It is natural to ask for the characterization of graphs with unbounded metric dimension.

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KW - basis

KW - convex polytope

KW - metric dimension

KW - resolving set

KW - wheel related graph

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Computing the metric dimension of convex polytopes generated by wheel related graphs

Abstract

Keywords

ASJC Scopus subject areas

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