弦環式網路之探討與研究

Abstract

「弦環式網路」是一種常被討論的區域網路架構 [1, 3, 8, 10, 11]。一個「無向的弦環式網路」是一個無向的三正則圖。在文獻[8, 10, 11]中，黃光明老師、陳尚寬學長、以及Wright，將「無向的弦環式網路」推廣成「有向的弦環式網路」，並給出計算「有向的弦環式網路」的直徑的方法。在文獻[3]中，陳尚寬學長、黃光明老師、以及劉昱綺學姊又推廣「有向的弦環式網路」來提出另一種有向的網路的連法，稱為「混合的弦環式網路」。雖然「無向的弦環式網路」的直徑已被完整地研究、並且可以運用公式得出，但是截至目前為止，「有向的弦環式網路」的直徑、以及「混合的弦環式網路」的直徑卻還未被完全找出來。在這篇論文裡，我們首先推導「有向的弦環式網路」以及「混合的弦環式網路」的同構性質；我們接著得出某些特殊的「有向的弦環式網路」以及「混合的弦環式網路」的直徑，與之前文獻不同的是，我們並不需要先計算出對應的「雙環式網路」的直徑來得出這些直徑。

Chordal ring networks have been proposed as a popular architecture for local area networks [1, 3, 8, 10, 11]. An undirected chordal ring network is an undirected regular graph of degree 3. In [8, 10, 11], Hwang, Chen, and Wright proposed the directed version of the undirected chordal ring network and derived the diameter of a directed chordal ring network. Furthermore, in [3], Chen et al. proposed the mixed chordal ring network. While the diameter of an undirected chordal ring network has been well studied [1], the diameter of a directed chordal ring network and the diameter of a mixed chordal ring network are not known. In this thesis, we shall study the isomorphism property of chordal ring networks and we shall find out the diameter of some directed chordal ring networks and the diameter of some mixed chordal ring networks.