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Fabricating Nanogaps by Nanoskiving

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Published on: May 13, 2013

Double edge resolving set and exchange property for nanosheet structure.

Ali N A Koam¹, Ali Ahmad², Sikander Ali³

¹Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi Arabia.

|March 6, 2024

Summary

This study investigates the edge metric dimension of nanosheet graphs from octagonal grids. It explores double-edge resolving sets and the exchange property, crucial for graph structure analysis.

Keywords:

Edge metric dimension Edge resolving set Exchange property edge resolving set Nanosheet Octogonal grid

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Area of Science:

Graph theory
Discrete mathematics
Chemical graph theory

Background:

The edge metric dimension is key for uniquely identifying graph edges using vertex subsets.
Nanosheet graphs derived from octagonal grids are relevant in materials science and nanotechnology.
Understanding resolving sets is vital for graph characterization.

Purpose of the Study:

To determine the edge metric dimension of nanosheet graphs constructed from octagonal grids.
To analyze the existence and properties of double-edge resolving sets in these graphs.
To explore the exchange property of edge resolving sets within this specific graph class.

Main Methods:

Utilizing graph theory principles to define and compute the edge metric dimension.
Applying set theory to identify and differentiate edge resolving sets.
Analyzing the structural properties of octagonal grid-based nanosheet graphs.

Main Results:

The edge metric dimension for octagonal grid-based nanosheet graphs is determined.
Conditions for the existence of double-edge resolving sets in these graphs are established.
The exchange property of edge resolving sets is investigated in this context.

Conclusions:

The edge metric dimension provides a valuable metric for analyzing nanosheet graph structures.
The findings contribute to the understanding of graph resolvability and its applications.
Further research into the exchange property can reveal deeper insights into graph properties.