What is the difference between cyclic and acyclic graph

The only wrinkle in all of this is that the meddling computer scientists have forced the term directed acyclic graph DAG on us. This refers to a digraph that contains no directed cycle although its underlying graph may contain a cycle. It's not a good name, but there's no putting that toothpaste back in the tube so we have to deal with its existence.

If a digraph contains a directed cycle, then that same walk in the underlying graph of the digraph would be a cycle. The converse is possible -- a digraph can be cyclic but not contain a directed cycle. The graph you pasted into your question is an example of that. Yes, as I just noted every directed cycle would be a cycle in the underlying graph. And a cycle in the underlying graph would be a directed cycle in the digraph iff its edges are all following the direction of the walk.

A cycle is a feature of the underlying graph, so the direction of the edges in the digraph is not considered. The good news is that all of this is essentially invisible once you have these definitions straight in your mind. Does this clear it up? Sign up to join this community. The best answers are voted up and rise to the top.

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There exists at least one path between every pair of vertices. Therefore, it is a connected graph. Disconnected Graph- A graph in which there does not exist any path between at least one pair of vertices is called as a disconnected graph.

Example- Here, This graph consists of two independent components which are disconnected. It is not possible to visit from the vertices of one component to the vertices of other component.

Therefore, it is a disconnected graph. Regular Graph- A graph in which degree of all the vertices is same is called as a regular graph. Examples- In these graphs, All the vertices have degree Therefore, they are 2-Regular graphs. Complete Graph- A graph in which exactly one edge is present between every pair of vertices is called as a complete graph.

Examples- In these graphs, Each vertex is connected with all the remaining vertices through exactly one edge. Therefore, they are complete graphs.

In a cycle graph, all the vertices are of degree 2. Examples- In these graphs, Each vertex is having degree 2. Therefore, they are cycle graphs. Cyclic Graph- A graph containing at least one cycle in it is called as a cyclic graph.

Example- Here, This graph contains two cycles in it. Therefore, it is a cyclic graph. Acyclic Graph- A graph not containing any cycle in it is called as an acyclic graph. Example- Here, This graph do not contain any cycle in it. Therefore, it is an acyclic graph. Finite Graph- A graph consisting of finite number of vertices and edges is called as a finite graph. Example- Here, This graph consists of finite number of vertices and edges.

Therefore, it is a finite graph. Infinite Graph- A graph consisting of infinite number of vertices and edges is called as an infinite graph. When following the graph from node to node, you will never visit the same node twice. This graph the thick black line is acyclic, as it has no cycles complete circuits. A connected acyclic graph, like the one above, is called a tree. What is meant by acyclic graph? An acyclic graph is a graph having no graph cycles. 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. What is cyclic and acyclic graph in data structure? A cyclic graph is a directed graph that contains a path from at least one node back to itself. An acyclic graph is a directed graph that contains absolutely no cycle; that is, no node can be traversed back to itself. Here, there are no paths which connect a node back to itself in the graph.

What is the meaning of acyclic? In a directed graph, the edges are connected so that each edge only goes one way. A directed acyclic graph means that the graph is not cyclic, or that it is impossible to start at one point in the graph and traverse the entire graph. Theorem: An undirected graph is acyclic iff a DFS yields no back edges. K4 is a maximal planar graph which can be seen easily. In fact, a planar graph G is a maximal planar graph if and only if each face is of length three in any planar embedding of G.

Corollary 1. A cyclic graph is bipartite iff all its cycles are of even length Skiena , p. Unfortunately, the term "cyclic graph" is sometimes also used in several other distinct and mutually incompatible ways in mathematics, especially outside graph theory.

It is for example sometimes used to mean a Hamiltonian graph , a graph isomorphic to a cycle graph , or a cycle graph itself Trudeau Some care is therefore needed when consulting the literature. Balaban, A. London: Academic Press, pp. Skiena, S. Reading, MA: Addison-Wesley,