Graph protection and domination

图形保护和控制包括设置警卫(或监视/广播设备，或紧急服务等)。在网络中的战略位置。网络中的位置可以由图的顶点来建模，如果网络中的相应位置在某种适当意义上彼此可达，则两个顶点是相邻的。守卫处理与其位置相邻的顶点上的问题(称为攻击)。根据保护模型的不同，警卫要么保持不动(这里的“警卫”可能指的是“广播塔”或“电力线上的智能服务器”)，要么移动到图的边缘以保护其他顶点免受攻击(或者救护车移动以处理紧急情况)；图中的每个顶点必须能够访问警卫(等等)。以这种方式。与警卫人数成正比的成本和效率之间存在冲突，平衡对立的力量是一个挑战。

Graph protection and domination involves the placement of guards (or surveillance/broadcasting equipment, or emergency services, etc.) at strategic positions in a network. Positions in a network can be modelled by vertices of a graph, two vertices being adjacent if the corresponding positions in the network are, in some appropriate sense, reachable from each other. The guards deal with problems (called attacks) at vertices adjacent to their positions. Depending on the protection model the guards either remain stationary ("guards" here could mean "broadcast towers" or "smart servers on power lines") or move across edges of the graph to defend other vertices against an attack (or an ambulance moves to deal with an emergency); every vertex of the graph must have access to a guard (etc.) in this way. There is a conflict between cost, which is proportional to the number of guards, and efficiency, and it is a challenge to balance the opposing forces.