Claw-free bricks that every b-invariant edge is solitary

Key Points

• Claw-free bricks exhibit unique characteristics in relation to b-invariant edges, particularly their solitary nature.
• The research develops criteria for identifying bricks beyond specific structures like K4, C6, and Petersen graph.
• A perfect matching is maintained after removing any two vertices in claw-free bricks, emphasizing their 3-connectedness.
• The exploration of b-invariant edges reveals structural insights that may aid future graph characterization efforts.