数学研究与评论
數學研究與評論
수학연구여평론
JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION
2005年
1期
58-63
,共6页
点可迁图%3限制边连通度%限制断片
點可遷圖%3限製邊連通度%限製斷片
점가천도%3한제변련통도%한제단편
vertex-transitive graph%3-restricted edge connectivity%restricted fragment
设G是阶至少为6的k正则连通图.如果G的围长等于3,那么它的3限制边连通度λ3(G)(≤)3k-6.当G是3或者4正则连通点可迁图时等号成立,除非G是4正则图并且λ3(G)=4.进一步,λ3(G)=4的充分必要条件是图G含有子图K4.
設G是階至少為6的k正則連通圖.如果G的圍長等于3,那麽它的3限製邊連通度λ3(G)(≤)3k-6.噹G是3或者4正則連通點可遷圖時等號成立,除非G是4正則圖併且λ3(G)=4.進一步,λ3(G)=4的充分必要條件是圖G含有子圖K4.
설G시계지소위6적k정칙련통도.여과G적위장등우3,나요타적3한제변련통도λ3(G)(≤)3k-6.당G시3혹자4정칙련통점가천도시등호성립,제비G시4정칙도병차λ3(G)=4.진일보,λ3(G)=4적충분필요조건시도G함유자도K4.
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 or4-regular connected vertex-transitive graph with the only exception that G is a 4-regular graphwith λ3(G) = 4. Furthermore, λ3(G) = 4 if and only if G contains K4 as its subgraph.
