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Characterization of 2-Path Product Signed Graphs with Its Properties
Deepa Sinha1, Deepakshi Sharma1
1Department of Mathematics, South Asian University, Akbar Bhawan Chanakyapuri, New Delhi 110021, India.
Computational Intelligence and Neuroscience
|August 2, 2017
Summary
This study introduces the 2-path product signed graph, defining its structure and edge signs based on vertex marks. It characterizes these graphs and explores properties like sign-compatibility and equivalence.
Area of Science:
- Graph theory
- Discrete mathematics
- Social network analysis
Background:
- Signed graphs represent relationships with positive (friendship) or negative (enmity) edges.
- Existing graph structures lack the specific properties of 2-path products.
Purpose of the Study:
- To define and characterize the 2-path product signed graph.
- To investigate properties such as sign-compatibility and equivalence.
Main Methods:
- Definition of the 2-path product signed graph based on paths of length two.
- Calculation of edge signs using vertex marks (product of incident edge signs).
- Analysis of graph properties including sign-compatibility and isomorphism.
Main Results:
- A formal characterization of 2-path product signed graphs is provided.
- Sign-compatibility and canonically-sign-compatibility are analyzed.
- Isomorphism and switching equivalence with 2-path signed graphs are discussed.
Conclusions:
- The paper establishes a foundational understanding of 2-path product signed graphs.
- Further research into their structural properties and applications is warranted.
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