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This is a Quantitative Study study.

October 16, 2025Open Access

Extremal graphs with minimum number of connected subgraphs in a given family

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Characterisation of graphs with minimum connected subgraphs in relation to vertex and cut vertices properties, suggesting novel classifications.

Graphs with minimum subgraph counts were characterized according to their vertices and cut vertex configurations, revealing intricate properties across varied parameters.
The identified graphs showcase minimum connected subgraphs across configurations with girth restrictions, enhancing understanding of these extremal graph properties.
Characterization applies comprehensively across the spectrum of cut vertex numbers, particularly within the range of 0 to 4, expanding existing graph theory frameworks.
These findings provide a foundational basis for further studies on extremal graph theory and the structural implications of vertex placements.

Pandey et al. (2025) studied this question.

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Characterisation of graphs with minimum connected subgraphs in relation to vertex and cut vertices properties, suggesting novel classifications.