On Metric Dimension of Subdivided Honeycomb Network and Aztec Diamond Network
Xiujun Zhang, Hafiz Muhammad Bilal, Atiq ur Rehman, Muhammad Tahir Hussain, Zhiqiang Zhang · Discrete Dynamics in Nature and Society · 2023
This paper investigates the metric dimensions of the polygonal networks, particularly, the subdivided honeycomb network, Aztec diamond as well as the subdivided Aztec diamond network. A 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, where n is the number of hexagons from a central point to the borderline of the network. A subdivided honeycomb network SHCN n is obtained by adding additional vertices on each edge of HCN n . An Aztec diamond network AZN n of order n is a lattice comprises of unit squares with center a , b satisfying a + b ≤ n . The subdivided Aztec diamond network SAZN n is obtained by adding additional vertices to each edge of AZN n . In this work, our main aim is to establish the results to show that the metric dimensions of SHCN n and AZN 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 HCN n and AZN n .