Computing dominant metric dimensions of certain connected networks.

Area of Science:

• Graph Theory
• Network Analysis
• Discrete Mathematics

Background:

• Metric dimension is a key distance-based parameter in network studies.
• Various types of metric dimensions have applications in chemistry and computer science.
• Dominant resolving sets offer advantages over resolving sets due to the property of domination.

Purpose of the Study:

• To compute the dominant metric dimension for wheel, gear, and anti-web wheel networks.
• To analyze the behavior of dominant metric dimension as network order increases.
• To highlight the relevance of these findings for robot navigation.

Main Methods:

• Utilizing graph theory principles to define and calculate metric dimensions.
• Applying distance-based parameters to analyze network structures.
• Deriving integral values for the dominant metric dimension of specific network types.

Main Results:

• The dominant metric dimension for wheel, gear, and anti-web wheel networks was successfully obtained in integral numbers.
• A bounded dominant metric dimension was observed as the order of these networks increases.
• The study provides specific values for these network topological parameters.

Conclusions:

• The dominant metric dimension of wheel, gear, and anti-web wheel networks is bounded and calculable.
• The findings are significant for applications like robot navigation and network analysis.
• This research contributes to understanding network properties through distance-based parameters.