点可迁图的限制边连通度

对于度k( ≥ 2 )的点可迁连通图的限制边连通度λ′,已知k≤λ′≤ 2k- 2 ,且λ′的界可以达到 .在此基础上 ,对度为k的点可迁图G进一步给出了满足λ′(G) =k的两个充要条件 .接着 ,对任意的连通图G0 证明了λ′(K2 ×G0 ) =min{2δ (G0 ) ,2λ′(G0 ) ,v(G0 ) }.最后证明了对任意满足 0≤s≤k- 3的整数s,存在度为k的点可迁连通图G满足λ′(G)=k s当且仅当k为奇数或者s为偶数

On Restricted Edge-Connectivity of Vertex-Transitive Graphs

It is known that for connected vertex-transitive graphs of degree k(≥2), the restricted edge-connectivity k≤λ′≤2k - 2 and the bounds can be attained. Two necessary and sufficient conditions for a vertex-transitive graph G of degree k to admit λ′(G) = k are presented. Afterwards, for any connected graph G0, λ′(K2 × G0) is determined to be λ′(K2×G0) = min {2δ(G0) ,2λ′(G0) ,v(G0)} , and then for any given integer s with 0 ≤s≤ k - 3, there is a connected vertex-transitive graph G of degree k and λ′(G) = k +s if and only if either k is odd or s is even.