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Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
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Connectivity Index of Generalized Uncertain Graph.

Jinchan Wang1, Xiulian Gao1, Xiaoshuang Zhou1

  • 1School of Mathematics and Big Data, Dezhou University, Dezhou 253023, China.

Computational Intelligence and Neuroscience
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This study introduces generalized uncertain graphs and a new algorithm to calculate their connectivity index, addressing indeterministic factors in graph theory. The research also defines and computes the alpha-connectivity index for these graphs.

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Area of Science:

  • Graph Theory
  • Uncertainty Theory
  • Network Analysis

Background:

  • Classical graph theory faces challenges with indeterministic factors.
  • Existing models may not adequately capture real-world network uncertainties.

Purpose of the Study:

  • To address indeterministic factors in connected graphs using uncertainty theory.
  • To introduce novel concepts and algorithms for uncertain graph connectivity.

Main Methods:

  • Employing uncertainty theory to model graph indeterminacy.
  • Developing and verifying a new algorithm for computing connectivity indices.
  • Defining and calculating the alpha-connectivity index for generalized uncertain graphs.

Main Results:

  • Introduction of generalized uncertain graphs and their connectivity index.
  • A validated algorithm for computing the connectivity index of uncertain and generalized uncertain graphs.
  • A proposed definition and algorithm for the alpha-connectivity index.

Conclusions:

  • The developed algorithms provide a robust method for analyzing uncertain graph connectivity.
  • Numerical experiments confirm the stability and efficiency of the proposed algorithms.
  • This work extends graph theory applications to systems with inherent uncertainty.