矩形碟狀蜂巢式網路

Abstract

在這篇論文當中，我們提出一個變形的蜂巢式網路。一個矩形碟狀蜂巢式網路HReD(m,n)是由矩形蜂巢式網路HReM(m,n)加上一環邊界所得到的。一矩形碟狀蜂巢式網路HReD(m,n)是一個三正則平面圖。矩形蜂巢式網路HReM(m,n)很明顯的是一個矩形碟狀蜂巢式網路HReD(m,n)的子圖。我們也證明一矩形碟狀蜂巢式網路HReD(m,n)為漢彌爾頓。此外，若是n大於等於6，則對任何f屬於V(HReD(m,n))聯集E(HReD(m,n))來說，HReD(m,n)-f仍是漢彌爾頓。

In this thesis, we propose a variation of honeycomb meshes. A honeycomb rectangular disk HReD(m,n) is obtained from the honeycomb rectangular mesh HReM(m,n) by adding a boundary cycle. A honeycomb rectangular disk HReD(m,n) is a 3-regular planar graph. It is obvious that the honeycomb rectangular mesh HReM(m,n) is a subgraph of HReD(m,n). We also prove that HReD(m,n) is hamiltonian. Moreover, HReD(m,n)-f remains hamiltonian for any f in V(HReD(m,n)) or E(HReD(m,n)) if n>=6.