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On derived t-path, t=2,3 signed graph and t-distance signed graph.

Deepa Sinha1, Sachin Somra1

  • 1Department of Mathematics, Faculty of Mathematics and Computer Science, South Asian University, New Delhi 110068, India.

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|February 3, 2025
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Summary
This summary is machine-generated.

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.

Keywords:
Balanced signed graphMarked signed graphSigned graphSwitching equivalencet-distance signed grapht-path product and t-distance signed grapht-path signed graph

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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.