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On the variable inverse sum deg index.

Edil D Molina1, Paul Bosch2, José M Sigarreta1

  • 1Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54 Col. Garita, 39650 Acalpulco Gro., Mexico.

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Summary
This summary is machine-generated.

This study characterizes graphs with maximum and minimum variable inverse sum deg indices (ISDa) for a < 0. These findings are relevant for understanding graph properties and their applications in chemical research.

Keywords:
degree-based topological indexinverse sum indeg indexoptimization on graphsvariable inverse sum deg index

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Area of Science:

  • Mathematical Chemistry
  • Graph Theory

Background:

  • Topological indices are crucial in mathematical chemistry, often calculated as sums over graph edges.
  • The variable inverse sum deg index (ISDa) is a significant topological index with various applications.

Purpose of the Study:

  • To solve problems posed by Vukičević regarding the ISDa index.
  • To characterize graphs with extremal ISDa index values for a < 0 within specific graph classes.
  • To assess the predictive power of the ISDa index in Quantitative Structure-Property Relationship (QSPR) analysis.

Main Methods:

  • Graph theory principles to define and analyze topological indices.
  • Extremal graph theory to determine maximum and minimum index values.
  • Quantitative Structure-Property Relationship (QSPR) analysis for property prediction.

Main Results:

  • Characterization of graphs with maximum and minimum ISDa index values for a < 0.
  • Identification of graph structures that optimize or minimize the ISDa index.
  • Demonstration of the ISDa index's predictive capability for physicochemical properties of polyaromatic hydrocarbons.

Conclusions:

  • The study provides a comprehensive characterization of graphs concerning the ISDa index for negative exponents.
  • The findings contribute to the understanding of graph invariants in chemical applications.
  • The ISDa index shows potential for predicting physicochemical properties in QSPR studies.