TY - JOUR

T1 - Notes on the Localization of Generalized Hexagonal Cellular Networks

AU - Azeem, Muhammad

AU - Jamil, Muhammad Kamran

AU - Shang, Yilun

PY - 2023/2/7

Y1 - 2023/2/7

N2 - The act of accessing the exact location, or position, of a node in a network is known as the localization of a network. In this methodology, the precise location of each node within a network can be made in the terms of certain chosen nodes in a subset. This subset is known as the locating set and its minimum cardinality is called the locating number of a network. The generalized hexagonal cellular network is a novel structure for the planning and analysis of a network. In this work, we considered conducting the localization of a generalized hexagonal cellular network. Moreover, we determined and proved the exact locating number for this network. Furthermore, in this technique, each node of a generalized hexagonal cellular network can be accessed uniquely. Lastly, we also discussed the generalized version of the locating set and locating number.

AB - The act of accessing the exact location, or position, of a node in a network is known as the localization of a network. In this methodology, the precise location of each node within a network can be made in the terms of certain chosen nodes in a subset. This subset is known as the locating set and its minimum cardinality is called the locating number of a network. The generalized hexagonal cellular network is a novel structure for the planning and analysis of a network. In this work, we considered conducting the localization of a generalized hexagonal cellular network. Moreover, we determined and proved the exact locating number for this network. Furthermore, in this technique, each node of a generalized hexagonal cellular network can be accessed uniquely. Lastly, we also discussed the generalized version of the locating set and locating number.

KW - locating set

KW - locating number

KW - resolving set

KW - fault-tolerant locating set

KW - generalized hexagonal cellular network

U2 - 10.3390/math11040844

DO - 10.3390/math11040844

M3 - Article

SN - 2227-7390

VL - 11

JO - Mathematics

JF - Mathematics

IS - 4

M1 - 844

ER -