Localisation of honeycomb rectangular torus

Abstract

The localisation of a network is the process of gaining access to a node's precise location or position. Using this technology, it is possible to determine the exact position of each network node in terms of a select few nodes within a subset. The locating set of a network is this subset, and the locating number of a network is its lowest cardinality. While the edge locating number is the same concept but on the bonds instead of nodes. In this work, we discussed some resolvability parameters such as locating number, edge locating number, fault-tolerant locating number and partition locating number of honeycomb rectangular torus. The honeycomb rectangular torus is very effective and innovative structure in chemical graph theory. This type of structure is being used in image processing, cellular phone base stations, computer graphics and more in mathematical chemistry.

Keywords:

• Localisation of honeycomb rectangular torus
• resolvability parameters
• locating number
• edge locating number
• fault-tolerant locating number
• partition locating number

2000 Mathematics Subject Classifications:

• 05C12
• 05C76

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

All the data supporting the results are included in the manuscript.