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The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
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An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
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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
PubMed
Summary
This summary is machine-generated.

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.

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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.