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The minimal-ABC trees with B1-branches
Darko Dimitrov1, Zhibin Du2, Carlos M da Fonseca3
1Hochschule für Technik und Wirtschaft Berlin, Wilhelminenhofstraße 75A, D-12459 Berlin, Germany.
Plos One
|April 19, 2018
Summary
The atom-bond connectivity (ABC) index characterizes molecular topology. This study shows minimal-ABC trees do not contain 4 or 3 B1-branches, advancing tree characterization.
Area of Science:
- Chemical graph theory
- Mathematical chemistry
- Molecular structure analysis
Background:
- The atom-bond connectivity (ABC) index is a key molecular descriptor linking chemistry and graph theory.
- It is widely applied in predicting bioactivity, chemical thermodynamics, and analyzing various chemical structures.
- Characterizing trees with minimal ABC index remains an open problem with significant research interest.
Purpose of the Study:
- To advance the characterization of trees with minimal atom-bond connectivity (ABC) index.
- To investigate the structural properties of trees that minimize the ABC index.
- To contribute to solving the open problem of minimal ABC index trees.
Main Methods:
- Graph theory principles applied to molecular structures.
- Analysis of tree structures and their topological indices.
- Investigating the impact of specific graph features (B1-branches) on the ABC index.
Main Results:
- Demonstrated that minimal-ABC trees cannot possess 4 B1-branches.
- Proved that minimal-ABC trees cannot possess 3 B1-branches.
- Initiated the analysis of minimal-ABC trees with 2 B1-branches.
Conclusions:
- Significant progress made towards the full characterization of minimal-ABC trees.
- Established constraints on the number of B1-branches in trees with the minimum ABC index.
- Opens avenues for further research into the structural properties of extremal trees in chemical graph theory.
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