Maximum size of connected graphs with bounded maximum degree and matching number

Key Points

• The study identifies bounds on the size of connected graphs based on their maximum degree and matching number.
• Findings show that as the maximum degree increases, the size of the graph can generally increase, with matching number constraints applied.
• Graph theory methods were used to analyze the structure and properties of connected graphs under specific constraints.
• These results highlight the intricate relationship between graph structure and optimization, suggesting avenues for further research.