Graph families | Perfect graphs

Cluster graph

In graph theory, a branch of mathematics, a cluster graph is a graph formed from the disjoint union of complete graphs.Equivalently, a graph is a cluster graph if and only if it has no three-vertex induced path; for this reason, the cluster graphs are also called P3-free graphs. They are the complement graphs of the complete multipartite graphs and the 2-leaf powers. The cluster graphs are transitively closed, and every transitively closed undirected graph is a cluster graph. (Wikipedia).

Cluster graph
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Graph (discrete mathematics) | If and only if | Cograph | Claw-free graph | Multipartite graph | Subcoloring | Transitive closure | Turán graph | Well-covered graph | Complement graph | Disjoint union of graphs | Graph theory | Maximal independent set | Induced subgraph | Leaf power | Block graph | Mathematics | Complete graph | Graph automorphism | Graph isomorphism | Induced path | Homogeneous graph | Parameterized complexity