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The Expected Values for the Gutman Index and Schultz Index in the Random Regular Polygonal Chains
1School of Mathematics and Big Data, Anhui University of Science & Technology, Huainan 232000, China.
Molecules (Basel, Switzerland)
|October 27, 2022
Summary
This study calculates exact formulas for the expected Gutman index and Schultz index in random regular polygonal chains. It also determines the average and extreme values for these topological indices.
Area of Science:
- Chemical Graph Theory
- Mathematical Chemistry
- Network Analysis
Background:
- The Gutman index and Schultz index are significant topological indices used in chemical graph theory.
- Understanding the properties of these indices in various molecular structures is crucial for predicting chemical compound behavior.
Purpose of the Study:
- To derive exact analytical formulae for the expected values of the Gutman index and Schultz index.
- To investigate the average and extremal values of these indices within the context of random regular polygonal chains.
Main Methods:
- Utilizing graph theory principles to define and analyze random regular polygonal chains.
- Applying combinatorial methods to calculate expected, average, and extremal values of topological indices.
Main Results:
- Exact analytical formulae for the expected Gutman index and Schultz index of random regular polygonal chains have been established.
- The study provides the range of possible values (average and extremal) for these indices in the considered structures.
Conclusions:
- The derived formulae offer precise tools for quantifying the topological properties of these specific molecular models.
- This research contributes to the broader understanding of structure-property relationships in chemical graph theory.
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