新疆大学学报（自然科学版）
新疆大學學報（自然科學版）
신강대학학보（자연과학판）
XINJIANG UNIVERSITY JOURNAL(NATURAL SCIENCE EDITION)
2011年
1期
14-22
,共9页
λ3-最优%直径%围长%超三限制性连通的%超三限制性边连通的
λ3-最優%直徑%圍長%超三限製性連通的%超三限製性邊連通的
λ3-최우%직경%위장%초삼한제성련통적%초삼한제성변련통적
λ-optimal%diameter%girth%super 3-restricted connected%super 3-restrictcd edge connected
图G是一个连通图.称X为三限制性割,如果G-X的每个连通分支至少有三个点.三限制性连通度k3(G)是三限制性割的最小基数,更进一步,如果图G的围长为4,去掉最小的三限制性割孤立出一条二长路,则称它是超三限制性连通的.本文给定了图是超三限制性连通的直径围长充分条件,还研究了超三限制性边连通图.
圖G是一箇連通圖.稱X為三限製性割,如果G-X的每箇連通分支至少有三箇點.三限製性連通度k3(G)是三限製性割的最小基數,更進一步,如果圖G的圍長為4,去掉最小的三限製性割孤立齣一條二長路,則稱它是超三限製性連通的.本文給定瞭圖是超三限製性連通的直徑圍長充分條件,還研究瞭超三限製性邊連通圖.
도G시일개련통도.칭X위삼한제성할,여과G-X적매개련통분지지소유삼개점.삼한제성련통도k3(G)시삼한제성할적최소기수,경진일보,여과도G적위장위4,거도최소적삼한제성할고립출일조이장로,칙칭타시초삼한제성련통적.본문급정료도시초삼한제성련통적직경위장충분조건,환연구료초삼한제성변련통도.
Let G=(V,E)be a connected graph.A vertex-cut X iS said to be a 3-restricted cut of G if G-X is not connected and every component of G-X has at least three vertices.The 3-restricted connectivity k3(G)of a connected graph G is defined as the minimum cardinality of a 3-restricted cut.Additionally,if G is a graph with girth g≥4 such that the deletion of every minimum 3-restricted cut isolates a 2-path,then G iS said to be super 3-restricted connected.In this paper,we give some sufficient conditions for a graph to be super 3-restricted connected in terms of the girth and the diameter,we also study super 3-restricted edge connected graph.
