南京大学学报(数学半年刊)
南京大學學報(數學半年刊)
남경대학학보(수학반년간)
JOURNAL OF NANJING UNIVERSITY MATHEMATICAL BIQUARTERLY
2006年
1期
36-44
,共9页
邻集并%泛连通性%边泛圈性
鄰集併%汎連通性%邊汎圈性
린집병%범련통성%변범권성
neighborhood union%panconnectivity%edge-pancyclicity
设G是一个顶点数为n(≥5)最小度为δ的2-连通简单图.本文证明了若图G的每一对距离为2的顶点u,v都满足|N(u)∪N(v)|≥n-δ+1,则除非G属于某些特殊图类,它的任意一对顶点x,y之间都存在长度从d(x,y)到n-1的路.
設G是一箇頂點數為n(≥5)最小度為δ的2-連通簡單圖.本文證明瞭若圖G的每一對距離為2的頂點u,v都滿足|N(u)∪N(v)|≥n-δ+1,則除非G屬于某些特殊圖類,它的任意一對頂點x,y之間都存在長度從d(x,y)到n-1的路.
설G시일개정점수위n(≥5)최소도위δ적2-련통간단도.본문증명료약도G적매일대거리위2적정점u,v도만족|N(u)∪N(v)|≥n-δ+1,칙제비G속우모사특수도류,타적임의일대정점x,y지간도존재장도종d(x,y)도n-1적로.
Let G be a 2-connected simple graph of order n (n ≥5) and minimum degree δ. This paper proves that if |N(u) ∪ N(v)| ≥ n - δ + 1 for each pair of vertices u, v of G at distance two, then for any two vertices x and y of G, there exist x-y paths of length from d(x, y) to n - 1 with a few exceptions.
