5元n立方体中指定三条点不交覆盖路

Specifying Three Disjoint Paths Covers in 5-ary n Cube

k元n立方体被视为将来候选网络结构之一,它有很多优良性质和参数,被用作度量路由选择,能直接影响网络通信的稳定性和传输时效.本文研究了5元n立方体中一对三条点不交覆盖路问题,运用数学归纳法可得,当n≥2时,在Q_(n)^(5)中任意取四个顶点x,y_(1),y_(2),y_(3),则在Q_(n)^(5)中存在三条内部顶点不交的覆盖路P1=(x,…,y_(1)),P2=(x,…,y_(2)),P3=(x,…,y_(3)).

k-ary n cube is regarded as one of the candidate network structures in the future.It has many excellent properties and parameters,which can be used to measure routing,and can directly affect the stability and transmission efficiency of network communication.In this paper,the problem of one to three disjoint coverage paths in 5-ary n cube.The following results are obtained by using mathematical induction:let Q_(n)^(5) be the 5-ary n cube,where n≥2,assume that x,y 1,y_(2),y_(3)be pairwise distinct vertices of Q_(n)^(5).Then Q_(n)^(5) can be found three vertex-disjoint covering paths P 1=(x,…,y_(1)),P 2=(x,…,y_(2)),P 3=(x,…,y_(3)).