3-Restricted Edge Connectivity of Vertex Transitive Graphs of Girth Three

Abstract:

      Let G be a k-regular connected graph of order at least six. If G has girth three, its 3-restricted edge connectivity λ₃(G) ≤3k-6. The equality holds when G is a cubic or 4-regular connected vertex-transitive graph with the only exception that G is a 4-regular graph with λ₃(G) = 4. Furthermore, λ₃(G) = 4 if and only if G contains K₄ as its subgraph.