有關對立圖形的探討

Abstract

在這篇論文中，我們探討對立圖形的特性，並藉由度數大於等於三的點，判斷一樹是否為對立圖形，最後證明Pn, Cn n ≥ 3 且 n = 4k; k ∈ N 家族的圖是對立圖形且Tn, Cn n ≥ 3 且n ̸= 4k; k ∈ N 家族的圖是對立圖形。

In this thesis, we use the number of vertices with degree greater than or equal to 3 as a criterion for trees being opposition graphs. Finally, we prove some families of graphs such as Pn, Cn with n ≥ 3 and n = 4k; k ∈ N are opposition graphs and some families of graphs such as Tn,\nCn with n ≥ 3 and n ̸= 4k; k ∈ N are not opposition graphs.