The Wide Diameter Formula of a Directed Double Loop Network

Abstract

给出了有向双环网络G(n;s1,s2)的宽直径公式,它由G(n;s1,s2)所确定的L-形瓦的4个参数a,b,p,q表示.令u=a-p,v=b-q,用D(G)与D2(G)分别表示G(n;s1,s2)的直径与宽直径,则(1)当u=1,v=1时,D2(G)=n-1.(2)当u>1,v>1时,D2(G)=D(G)+1=max{a+b-p-1,a+b-q-1}.(3)当u=1,v>1时,D2(G)=「b-1/v」+a+v-2.(4)当u>1,v=1时,D2(G)=「a-1/u」+b+u-2.In this paper,the wide diameter formula for a directed double-loop network G(n;s1,s2) is given.It is represented by four parameters a,b,p,q of the L-shape tile determined by the network G(n;s1,s2).Let u=a-p,v=b-q,and D(G) and D2(G) denote the diameter and the wide diameter of G(n;s1,s2) respectively.It is proved that (1)If u=1,v=1,then D2(G)=n-1.(2)If u>1,v>1,then D2(G)=D(G)+1=max{a+b-p-1,a+b-q-1}.(3)If u=1,v>1,then D2(G)= 「b-1/v」+a+v-2.(4)If u>1,v=1,then D2(G)=「a-1/u」+b+u-2.福建省科技三项经费(2006F5068);; 福建省自然科学基金(S0650036)资

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