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Expected Value of Multiplicative Degree-Kirchhoff Index in Random Polygonal Chains
Xinmei Liu1, Xinfeng Liang1, Xianya Geng1
1School of mathematics and big data, Anhui University of Science and Technology, 232001 Huainan, China.
This study provides exact formulas for the expected value of the multiplicative degree-Kirchhoff index in random polygonal chains. These findings help determine extremal and average values for this important topological index.
Area of Science:
- Mathematics
- Graph Theory
- Chemical Graph Theory
Background:
- The multiplicative degree-Kirchhoff index is a key topological index in chemical graph theory.
- Understanding its properties in random structures is crucial for molecular characterization.
Purpose of the Study:
- To derive exact formulas for the expected value of the multiplicative degree-Kirchhoff index in random polygonal chains.
- To determine the extremal and average values of this index for all polygonal chains.
Main Methods:
- Utilizing mathematical and graph-theoretic approaches.
- Developing exact formulas for expected values in stochastic graph models.
Main Results:
- Established precise formulas for the expected multiplicative degree-Kirchhoff index in random polygonal chains.
- Identified the specific polygonal chains exhibiting extremal (maximum and minimum) and average values of this index.
Conclusions:
- The derived formulas offer a quantitative method for analyzing the multiplicative degree-Kirchhoff index in random networks.
- This research contributes to the understanding of topological indices in complex molecular structures.
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