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A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
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Interval-valued bipolar fuzzy line graphs.

Keneni Abera Tola1, V N Srinivasa Rao Repalle2, Mamo Abebe Ashebo2

  • 1Department of Mathematics, Wollega University, Nekemte, Ethiopia. keneniabera460@gmail.com.

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|June 26, 2023
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Summary
This summary is machine-generated.

This study introduces the interval-valued bipolar line fuzzy graph (IVBFLG), enhancing flexibility in modeling complex, time-dependent networks. Researchers characterized IVBFLGs and explored their properties, offering new tools for network analysis.

Keywords:
Bipolar fuzzy graphInterval-valued bipolar fuzzy graph IsomorphismInterval-valued bipolar fuzzy line graph

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Area of Science:

  • Graph Theory
  • Fuzzy Mathematics
  • Network Science

Background:

  • Bipolar models offer advantages over classical and fuzzy models.
  • Interval-valued bipolar fuzzy graphs (IVBFGs) are useful for time-dependent network problems.
  • Existing fuzzy graph models lack the flexibility of bipolar approaches for human thinking.

Purpose of the Study:

  • Introduce the novel concept of interval-valued bipolar line fuzzy graphs (IVBFLGs).
  • Explore the fundamental properties and characterizations of IVBFLGs.
  • Investigate relationships between IVBFLGs and their corresponding IVBFGs.

Main Methods:

  • Definition and characterization of IVBFLGs.
  • Development and proof of propositions and theorems for IVBFLGs.
  • Analysis of isomorphisms between IVBFLGs and IVBFGs.
  • Investigation of IVBFLG properties: degree, size, order, regularity, strength, and completeness.

Main Results:

  • The concept of IVBFLG is formally proposed and defined.
  • Characterizations and key properties of IVBFLGs are established.
  • Conditions for isomorphism between IVBFGs and their corresponding IVBFLGs are derived.
  • Examples are provided to illustrate the proposed concepts and properties.

Conclusions:

  • IVBFLGs extend the utility of IVBFGs for complex network analysis.
  • The study provides a theoretical foundation for IVBFLGs with demonstrated properties.
  • The findings offer new insights into network structures with time-dependent and bipolar characteristics.