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 w...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.展开更多
文摘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.
