High Quality Content by WIKIPEDIA articles! In graph theory, a threshold graph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations: 1. Addition of a single isolated vertex to the graph. 2. Addition of a single dominating vertex to the graph, i.e. a single vertex that is connected to all other vertices. For example, the graph of the figure is a threshold graph. It can be constructed by beginning with a single-vertex graph (vertex 1), and then adding black vertices as isolated vertices and red vertices as dominating vertices, in the order in which they are numbered.

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