Open Access

ARTICLE

Edge Metric Dimension of Honeycomb and Hexagonal Networks for IoT

by Sohail Abbas¹, Zahid Raza², Nida Siddiqui², Faheem Khan³, Taegkeun Whangbo^3,*

1 Department of Computer Science, College of Computing and Informatics, University of Sharjah, Sharjah, 27272, UAE
2 Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, 27272, UAE
3 Artificial Intelligence Lab, Department of Computer Engineering, Gachon University, Seongnam, 13557, Korea

* Corresponding Author: Taegkeun Whangbo. Email:

(This article belongs to the Special Issue: Advancements in Lightweight AI for Constrained Internet of Things Devices for Smart Cities)

Computers, Materials & Continua 2022, 71(2), 2683-2695. https://doi.org/10.32604/cmc.2022.023003

Received 25 August 2021; Accepted 27 September 2021; Issue published 07 December 2021

Abstract

Wireless Sensor Network (WSN) is considered to be one of the fundamental technologies employed in the Internet of things (IoT); hence, enabling diverse applications for carrying out real-time observations. Robot navigation in such networks was the main motivation for the introduction of the concept of landmarks. A robot can identify its own location by sending signals to obtain the distances between itself and the landmarks. Considering networks to be a type of graph, this concept was redefined as metric dimension of a graph which is the minimum number of nodes needed to identify all the nodes of the graph. This idea was extended to the concept of edge metric dimension of a graph G, which is the minimum number of nodes needed in a graph to uniquely identify each edge of the network. Regular plane networks can be easily constructed by repeating regular polygons. This design is of extreme importance as it yields high overall performance; hence, it can be used in various networking and IoT domains. The honeycomb and the hexagonal networks are two such popular mesh-derived parallel networks. In this paper, it is proved that the minimum landmarks required for the honeycomb network HC(n), and the hexagonal network HX(n) are 3 and 6 respectively. The bounds for the landmarks required for the hex-derived network HDN1(n) are also proposed.

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Keywords

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