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ali kadum
ali kadum

Reputation: 3

What do we call a disconnected graph, with cycles

I know that A forest is when they are disconnected, however with no cycles. Graphs are connected, and may have a cycle. However, I do not know what a disconnected graph, with cycles is called.

Upvotes: 0

Views: 260

Answers (1)

leonardkraemer
leonardkraemer

Reputation: 6813

You can call it disjoint union of graphs or simply disconnected graph (see also http://mathworld.wolfram.com/DisconnectedGraph.html)

There are also some subclasses:

Certain special classes of graphs may be represented using disjoint union operations. In particular:

  1. The forests are the disjoint unions of trees.
  2. The cluster graphs are the disjoint unions of complete graphs.
  3. The 2-regular graphs are the disjoint unions of cycle graphs.

More generally, every graph is the disjoint union of connected graphs, its connected components.

The cographs are the graphs that can be constructed from single-vertex graphs by a combination of disjoint union and complement operations.

Couls also be:

A pseudoforest is an undirected graph in which every connected component contains at most one graph cycle.

Upvotes: 1

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