摘要: | 在本篇論文中,我們定義了: 1.D(Kp,q,r,s)={(u,v)| Kp,q,r,s=uC3+vC4} 2.S(Kp,q,r,s)={(u,v)| 3u+4v=|E(Kp,q,r,s)|}
由於p,q,r,s之間的大小關係,有著各種不同情況,因此我們分別分成下列幾種情況來討論,我們證明了: 1.D(K4(p))=S(K4(p)) 2.D(Kp,p,p,s)=S(Kp,p,p,s) 3.當p≠4,12時,則D(Kp,p,s,s)=S(Kp,p,s,s) 4.當p≠4,12時,則D(Kp,p,r,s)=S(Kp,p,r,s) 5.當p、q、r、s均相異的情形時,我們獲得了下面一些結果: (i)當m≠4,12,u≦40m*m,則D(K2m,4m,6m,8m)=S(K2m,4m,6m,8m) (ii)當m≠4,12,m>n,u≦8m*m+32mn,則D(K2m,4m,6m,8n)=S(K2m,4m,6m,8n) (iii)當m≠4,12,m>n,u≦8m*m+32mn,則D(K2m,4m,6n,8m)=S(K2m,4m,6n,8m) (iv)當m≠4,12,m>n,u≦12m*m-28mn,則D(K2m,4n,6m,8m)=S(K2m,4n,6m,8m) (v)當m≠4,12,m>n,u≦24m*m+16mn,則D(K2n,4m,6m,8m)=S(K2n,4m,6m,8m) In this thesis,we define: 1.D(Kp,q,r,s)={(u,v)| Kp,q,r,s=uC3+vC4} 2.S(Kp,q,r,s)={(u,v)| 3u+4v=|E(Kp,q,r,s)|} According the relations among p,q,r,s, we have the following: 1.D(K4(p))=S(K4(p)) 2.D(Kp,p,p,s)=S(Kp,p,p,s) (3) When p≠4,12 ,then D(Kp,p,s,s)=S(Kp,p,s,s) (4) When p≠4,12 ,then D(Kp,p,r,s)=S(Kp,p,r,s) (5) p,q,r,s are all different: (i)When m≠4,12,u≦40m*m,then D(K2m,4m,6m,8m)=S(K2m,4m,6m,8m) (ii)When m≠4,12,m>n,u≦8m*m+32mn,then D(K2m,4m,6m,8n)=S(K2m,4m,6m,8n) (iii)When m≠4,12,m>n,u≦8m*m+32mn,then D(K2m,4m,6n,8m)=S(K2m,4m,6n,8m) (iv)When m≠4,12,m>n,u≦12m*m-28mn,then D(K2m,4n,6m,8m)=S(K2m,4n,6m,8m) (v)When m≠4,12,m>n,u≦24m*m+16mn,then D(K2n,4m,6m,8m)=S(K2n,4m,6m,8m) |