對於一個網路圖，將其每一個邊分配一個顏色數字，若此圖的任何兩點之間都存在一條所有邊的顏色都不重複的路徑，則此圖稱為彩虹連結圖，而所使用顏色的最少數量被稱為彩虹連結數。
彩虹連結數是由Chartrand等學者於2008年所提出，至今已有許多學者針對不同的網路圖，例如輪圖、彼德森圖和完全圖等等，進行有關彩虹連結數的研究。而根據已知文獻，目前尚未有人提出對於三角化金字塔網路圖的彩虹連結數之研究成果，所以本論文探討三角化金字塔網路圖的拓樸特性以決定其彩虹連結數。
Rainbow connection number of a connected graph G is the minimum number of colors needed to color the edges of G, so that every pair of vertices is connected by at least one path whose edges have distinct colors.
The concept of rainbow connection was introduced by Chartrand et al. in 2008. Many scholars are interested in rainbow connection problem and have results on graphs, such as wheel graphs, Peterson graphs, complete graphs, pyramid networks etc. According to the known literature, there has not yet been anyone to propose about rainbow connection number of the triangular pyramid networks. In this paper, we propose a minimum rainbow coloring for a triangular mesh. Based on the modification of the edge coloring for triangular meshes, we further determine the rainbow connection number of a triangular pyramid.
