On metric dimension of flower graphs fnχm and convex polytopes

Simple item page
dc.contributor.authorImran, Muhammad
dc.contributor.authorFozia Bashir
dc.contributor.authorBaig, Abdul Q.
dc.contributor.authorBokhary, Ahtsham Ul Haq
dc.contributor.authorAyesha Riasat
dc.contributor.authorTomescu, Ioan
dc.date.accessioned2014-04-14T14:22:53Z
dc.date.available2014-04-14T14:22:53Z
dc.date.issued2013
dc.description.abstractLet G be a connected graph and d(x, y) be the dis-tance between the vertices x and y. A subset of vertices W ={w1,w2, · · · ,wk} is called a resolving set for G if for every two distinct vertices x, y ∈ V (G), there is a vertex wi ∈ W such that d(x,wi) 6= d(y,wi). A resolving set containing a minimum number of vertices is called a metric basis for G and the number of vertices in a metric basis is its metric dimension dim(G). Let F be a family of connected graphs Gn : F = (Gn)n 1 depend- ing on n as follows: the order |V (G)| = '(n) and lim n!1 '(n) = ∞. If there exists a constant C > 0 such that dim(G) ≤ C for every n ≥ 1 then we shall say that F has bounded metric dimension; otherwise F has unbounded metric dimension. If all graphs in F have the same metric dimension (which does not depend on n), then F is called a family with constant metric dimension. The metric dimension of some classes of plane graphs has been de- termined in [3], [4], [5], [10], [12], [15] and [22], while metric dimen- sion of some classes of convex polytopes has been studied in [10]. In this paper this study is extended, by considering flower graphs fn×m and two classes of graphs associated to convex polytopes.en_US
dc.identifier.citationImran, M., Bashir, F., Baig, A. Q., Ul, S. A., Bokhary, H., Riasat, A., & Tomescu, I. (2013). On metric dimension of flower graphs fnχm and convex polytopes. Utilitas Mathematica, 289-409.en_US
dc.identifier.urihttps://escholar.umt.edu.pk/handle/123456789/1116
dc.language.isoenen_US
dc.publisherUtilitas Mathematicaen_US
dc.subjectMetric Dimensionen_US
dc.subjectBasisen_US
dc.subjectResolving seten_US
dc.subjectConvex polytopesen_US
dc.subjectFlower graphsen_US
dc.titleOn metric dimension of flower graphs fnχm and convex polytopesen_US
dc.typeArticleen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
On metric dimension of flower graphs and convex polytopes.pdf
Size:
58.42 KB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.71 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
Department of Social Sciences