故障超立方体中经过指定路的无故障圈  

Fault-free Cycles Passing Through a Prescribed Path in a Faulty Hypercube

作　　者：陈协彬[1] 方来金[1] 

机构地区：[1]漳州师范学院数学与信息科学系,福建漳州363000

出　　处：《数学研究》2010年第3期286-292,共7页Journal of Mathematical Study

基　　金：福建省自然科学基金资助项目(2010J01354)

摘　　要：研究了在含有故障点和（或）故障边的n维超立方体Qn中经过给定路的无故障圈问题,得到以下结果：设Fv V（Qn）,Fe E（Qn）.若｜Fv｜＋｜Fe｜≤n-h且3≤h≤n,或｜Fv｜＋｜Fe｜≤n-3且h=2,则在Qn-Fv-Fe中,每一条长度等于h的路P都包含在每个偶长度从2h＋2到2^n-2｜Fv｜的圈中.并且若又有条件｜Fv｜＋｜Fe｜〈h-1时,则路P还包含在长度等于2h的无故障的圈中.In this paper,we consider the problem of fault-free cycles passing through a prescribed path in a hypercube Qn with mixed node and edge failures.We obtain the following result：Let Fv V（Qn）,Fe E（Qn）.If ｜Fv｜ ＋ ｜Fe｜≤n- h and 3≤h≤n or ｜Fv｜ ＋ ｜Fe｜≤n - 3 and h = 2,then every path P of length h lies on a cycle in Qn - Fv - Fe of every even length from 2h ＋ 2 to 2~n - 2｜Fv｜ inclusive.Moreover,the path P lies on a cycle in Qn - Fv - Fe of length 2h if the additional condition ｜Fv｜ ＋ ｜Fe｜h - 1 holds.

关 键 词：互联网络 超立方体 路 圈 容错 

分 类 号：O157.5[理学—数学]