Which Graphs Are Acyclic?

David Miller
David Miller
• • 6 min read

An Acyclic Graph Is a Graph Having No Graph Cycles Graph Cycles Graph Classes Defined by cyclesBipartite Graph, a Graph Without Odd Cycles (Cycles with an Odd...

Which Graphs Are Acyclic?

An acyclic graph is a graph having no graph cycles

graph cycles
Graph classes defined by cycles

Bipartite graph, a graph without odd cycles (cycles with an odd number of vertices). Cactus graph, a graph in which every nontrivial biconnected component is a cycle. Cycle graph, a graph that consists of a single cycle. Chordal graph, a graph in which every induced cycle is a triangle.

› wiki › Cycle_(graph_theory)
. Acyclic graphs are bipartite. A connected acyclic graph is known as a tree, and a possibly disconnected acyclic graph is known as a forest (i.e., a collection of trees).

How can you tell if a graph is acyclic?

To test a graph for being acyclic:
  1. If the graph has no nodes, stop. The graph is acyclic.
  2. If the graph has no leaf, stop. The graph is cyclic.
  3. Choose a leaf of the graph. Remove this leaf and all arcs going into the leaf to get a new graph.
  4. Go to 1.

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Can a graph be cyclic acyclic or both?

A cyclic graph is a graph containing at least one graph cycle. A graph that is not cyclic is said to be acyclic. A cyclic graph possessing exactly one (undirected, simple) cycle is called a unicyclic graph.

David Miller

David Miller

Executive Financial & Market Analyst
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David Miller brings 15 years of experience in global economics, personal finance strategy, and market dynamics. He specializes in turning complex economic trends into actionable insights for everyday readers.