由一個荷米爾遜圖建構偏序集

Abstract

在這篇論文裡，我們專注在漢米爾頓圖上。首先由一個半徑為D的漢 米爾頓圖建構一個偏序集P。在P中的元素同構於半徑小於D 的漢米 爾頓圖。我們從反面來定義P。我們也獲得一些P 的計算性質。然後， 我們試著在P中建構一個Z字型的結構，計算在P中有多少Z字型。 我們也計算在一些條件下Z 字型的數目。

In this thesis, we focus on Hermitian forms graphs. Firstly, we construct a poset P from a Hermitian forms graph Herq(D), where D is the diameter. The elements in P are those subgraphs of Herq(D) which are isomorphic to Herq(t) for 0<t<D. We order P by reversed inclusion. Some counting properties of P are obtained. Then, we try to construct a zigzag-like structure in P so that we can count the number of zigzags inside P. We also count the number of zigzags in some conditions.