Open Access
ARTICLE
Edge Metric Dimension of Honeycomb and Hexagonal Networks for IoT
Sohail Abbas1, Zahid Raza2, Nida Siddiqui2, Faheem Khan3, Taegkeun Whangbo3,*
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.
Keywords
Cite This Article
APA Style
Abbas, S., Raza, Z., Siddiqui, N., Khan, F., Whangbo, T. (2022). Edge metric dimension of honeycomb and hexagonal networks for iot. Computers, Materials & Continua, 71(2), 2683-2695. https://doi.org/10.32604/cmc.2022.023003
Vancouver Style
Abbas S, Raza Z, Siddiqui N, Khan F, Whangbo T. Edge metric dimension of honeycomb and hexagonal networks for iot. Comput Mater Contin. 2022;71(2):2683-2695 https://doi.org/10.32604/cmc.2022.023003
IEEE Style
S. Abbas, Z. Raza, N. Siddiqui, F. Khan, and T. Whangbo "Edge Metric Dimension of Honeycomb and Hexagonal Networks for IoT," Comput. Mater. Contin., vol. 71, no. 2, pp. 2683-2695. 2022. https://doi.org/10.32604/cmc.2022.023003