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On derived t-path, t=2,3 signed graph and t-distance signed graph
1Department of Mathematics, Faculty of Mathematics and Computer Science, South Asian University, New Delhi 110068, India.
Methodsx
|February 3, 2025
Summary
This study introduces the t-path product signed graph and t-distance signed graph, offering new characterizations for switching equivalence. These models aid in developing real-world communication network applications.
Area of Science:
- Graph Theory
- Discrete Mathematics
- Network Analysis
Background:
- Signed graphs are fundamental in representing relationships with positive or negative values.
- Understanding graph products and distances is crucial for network analysis.
Purpose of the Study:
- To introduce and characterize t-path product signed graphs.
- To characterize t-distance signed graphs and their switching equivalence.
- To explore applications in communication networks.
Main Methods:
- Definition of t-path product signed graphs based on paths of length t.
- Definition of t-distance signed graphs based on paths of length 2.
- Characterization of switching equivalence for these graph types.
Main Results:
- Provided characterizations for signed graphs switching equivalent to t-path product signed graphs.
- Characterized signed graphs switching equivalent to t-distance signed graphs.
- Established the foundation for modeling real-world problems using t-path networks.
Conclusions:
- The characterizations offer new insights into the structure of signed graphs.
- t-path and t-distance signed graphs provide valuable tools for network modeling.
- These concepts have potential applications in communication networks and beyond.
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