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On tricyclic graphs with maximum atom-bond sum-connectivity index
Sadia Noureen1, Rimsha Batool1, Abeer M Albalahi2
1Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, Pakistan.
Heliyon
|August 7, 2024
Summary
This study investigates the atom-bond sum-connectivity (ABS) index in connected tricyclic graphs. Researchers identified graphs with the maximum ABS index, expanding on previous work that focused on minimum values.
Area of Science:
- Chemical Graph Theory
- Mathematical Chemistry
- Network Analysis
Background:
- Topological indices like sum-connectivity, Randić, and atom-bond connectivity are crucial in analyzing molecular structures based on vertex degrees.
- The atom-bond sum-connectivity (ABS) index is a recently developed variant of these established topological indices.
- Prior research (Zuo et al., 2024) determined graphs with the minimum ABS index for connected tricyclic graphs with maximum degree up to 4.
Purpose of the Study:
- To determine the connected tricyclic graphs that exhibit the maximum possible value of the atom-bond sum-connectivity (ABS) index.
- To extend the understanding of extremal graph properties related to the ABS index within a specific class of graphs.
Main Methods:
- Analysis of connected tricyclic graphs of order n.
- Focus on characterizing graphs with extremal (maximum) ABS index values.
- Building upon existing graph theory principles and recent findings on minimum ABS index.
Main Results:
- Identification of specific structures of connected tricyclic graphs that yield the highest ABS index.
- Characterization of the extremal graphs concerning the atom-bond sum-connectivity index.
Conclusions:
- The study successfully characterizes connected tricyclic graphs with the maximum ABS index.
- This research contributes to the field of chemical graph theory by providing insights into extremal topological indices.
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