把Torus Cordalis Network G看作是一個電腦網路分佈圖，其中每個點代表一台電腦，連接兩點的邊代表連接兩台電腦的網路。 我們在本篇論文內考慮在G上電腦病毒傳染的數學模型。 我們在G上電腦病毒傳染的過程如下: 一開始圖G上有些點被塗成白色(代表健康)，剩下的點被塗成黑色(代表被感染)。 我們先假設一個點變成黑色後它就永遠無法重回白色。 在離散的時間 t 時，每個白點會被在前一個時間 (t-1) 時較多鄰居已經的被塗的顏色重新著色，否則它依然是白色的。在本篇論文中，給定一個Torus Cordalis Networks G後，我們研究一開始要令G上多少點塗成黑色(代表被感染)才能在最後將G上所有點感染為黑色。 Let G = (V,E) be a connected computer network, where a vertex represents a computer and each edge between two vertices represents a cable connecting them. We consider a mathematical model of “computer virus” propagation on G, where computer viruses are small computer programs that can infect computers. Consider the following repetitive process on G: Initially, each vertex is colored white (healthy) or black (infected). The set of initial black vertices is called a seed. We assume that once a vertex becomes black, it remains black forever. At each discrete time step, each white vertex is recolored by the color shared by the majority of vertices in its neighborhood, at the previous time step; in case of tie, it remains white. The process runs until either all vertices become black or no additional white vertices can be infected. The minimum number of virus seeds for G is denoted by B(G). In this paper, we study B(G) for torus cordalis graphs G. Our work improves some results of Flocchini, Lodi, Luccio, Pagli and Santoro (Dynamic monopolies in tori, Discrete Applied Mathematics 137 (2004) 197-212).
