On metric dimension of tridecagonal circular ladder

Sahil Sharma, Malkesh Singh, Vijay Kumar Bhat

Abstract


In n-dimensional space, convex polytopes are geometric objects characterised by straight edges and flat faces. They are a fascinating and significant challenge in many branches of mathematics and its applications because of their convexity, simplicity, and rich mathematical features. Let G = (V, E) be a simple, connected and undirected graph of order h. Let B be an ordered subset of the set of vertices V (G). If vector of distances of disticnt vertices of G with respect to the set B are distinct, then the set B is referred as resolving set or vertex resolving set for the graph G. A resolving set for G with least possible cardinality is termed as metric basis for G and the number of elements in a metric basis for G is known as the metric dimension of the graph G. In this manuscript, we prove that the metric dimension is three for two closely related families of convex polytopes.

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References


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DOI: https://doi.org/10.52846/ami.v52i2.2056