### 博碩士論文 972201009 詳細資訊

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(On the Spread of Viruses on Torus Cordalis Networks)

 ★ 以2D HP 模型對蛋白質摺疊問題之研究 ★ On Steiner centers of graphs ★ On the Steiner medians of a block graph ★ 圖形列表著色 ★ 秩為5的圖形 ★ Some results on distance-two labeling of a graph ★ 關於非奇異線圖的樹 ★ On Minimum Strictly Fundamental Cycle Basis ★ 目標集選擇問題 ★ 路徑圖與格子圖上的目標集問題 ★ 超立方體圖與格子圖上的目標集問題 ★ 圖形環著色數的若干等價定義 ★ 網格圖上有效電阻計算方法的比較 ★ 數樹：方法綜述 ★ d 維立方體圖上有效電阻與首達時間的計算方法

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).

★ 網路
★ 病毒散播

★ Spread of Viruses
★ Network

1 Introduction and preliminaries 1
2 Main results 4
References 34

manuscript,2010.
[2] Paola Flocchini, Elena Lodi, Fabrizio Luccio, Linda Pagli
and Nicola Santoro, Dynamic monopolies in tori, Discrete
Applied Mathematics 137 (2004) 197-212.
[3] D. Peleg, Size bounds for dynamic monopolies, Discrete
Applied Mathematics 86 (1998) 263-273.