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Xiujun  Zhang
Xiujun Zhang

Public Documents 1
On Metric Dimension of Subdivided Honeycomb Network and Aztec Diamond Network
Xiujun  Zhang
Muhammad Bilal

Xiujun Zhang

and 4 more

September 12, 2022
This paper investigates the metric dimensions of the polygonal networks, particularly, of subdivided honeycomb network as well as Aztec diamond network. The polygon is any two-dimensional shape formed by straight lines. Triangles, quadrilaterals, pentagons and hexagons are all representations of polygons. For instance, hexagons help us in many models to construct honeycomb network (HCN (n)), where n is the number of hexagons from a central point to the borderline of the network. Subdivided honeycomb network (SHCN (n)) is obtained by adding additional vertices on each edge of HCN (n). An Aztec diamond network (AZ N (n)) of order n is a lattice comprises of unit squares with center (a, b) satisfying |a | + |b| ≤ n. In this work, our main aim is to establish the results to show that the metric dimensions of SHCN (n) and AZ N (n) are 2 and 3 for n = 1 and n ≥ 2, respectively. In the end, some open problems are listed with regard to metric dimensions for k -subdivisions of SHCN (n) and AZ N (n).

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