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Solutions of Detour Distance Graph Equations.
S Celine Prabha1, M Palanivel2, S Amutha3
1Department of Mathematics, RMD Engineering College, Chennai 601 206, Tamil Nadu, India.
Sensors (Basel, Switzerland)
|November 11, 2022
Summary
This study solves graph equations for detour distance and antipodal graphs, extending graph theory applications in wireless sensor networks. The findings contribute to understanding complex network relationships through mathematical modeling.
Area of Science:
- Mathematics
- Computer Science
- Network Theory
Background:
- Graph theory models pairwise relations in wireless sensor networks.
- Graph equations involve unknown graph structures.
- Many graph theory problems are formulated using graph equations.
Purpose of the Study:
- To solve specific graph equations involving detour distance and antipodal graphs.
- To extend the application of graph equations in network analysis.
- To investigate the relationship between these graph types and line graphs.
Main Methods:
- Utilized principles of graph theory to define and analyze graph equations.
- Developed methods for solving equations related to detour two-distance graphs.
- Applied techniques to solve equations for detour three-distance graphs and detour antipodal graphs.
- Incorporated the concept of line graphs into the equation-solving process.
Main Results:
- Successfully solved a class of graph equations for detour two-distance graphs.
- Provided solutions for graph equations involving detour three-distance graphs.
- Determined solutions for graph equations of detour antipodal graphs.
- Established connections between these graph structures and their line graph counterparts.
Conclusions:
- The paper successfully solves complex graph equations for detour and antipodal graphs.
- The results enhance the utility of graph equations in modeling network structures.
- This research contributes to the mathematical understanding of wireless sensor networks.
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